Receiving Helpdesk

how do you write an inequality for a graph

by Davonte Stamm Published 3 years ago Updated 2 years ago

How do you write an inequality for a graph?

  • Rearrange the equation so "y" is on the left and everything else on the right.
  • Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
  • Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).

Part of a video titled How to Write Linear Inequalities from Graph | Algebra - YouTube
4:21
10:57
Type in y. Less than equal to negative and now you can either put 1x. Since it's a fraction you canMoreType in y. Less than equal to negative and now you can either put 1x. Since it's a fraction you can write the 1 or you can just put x divided. By 2 for the slope. And then our y-intercept was 4.

Full Answer

What are the steps to graphing an inequality?

Steps on Graphing Linear Inequalities

  1. Always start by isolating the variable \color {red}y on the left side of the inequality.
  2. Change the inequality to equality symbol. For now, you will deal with a line.
  3. Graph the boundary line from step 2 in the XY- plane. ...
  4. The last step is to shade one side or region of the boundary line. ...

More items...

How do you find an inequality on a graph?

You can use clues from the graph, together with your knowledge of lines and linear relationships, to find an equation for the inequality. Check whether the inequality line is dotted or solid. If dotted, it is a less-than or greater-than inequality.

How will you graph the solution of an inequality?

Method 3 of 3: Graphing a Quadratic Inequality on a Coordinate Plane

  1. Determine whether you have a quadratic inequality.
  2. Graph the line on a coordinate plane. To do this, turn the inequality into an equation, and graph the line as you normally would.
  3. Draw the parabola.
  4. Find some test points. ...
  5. Shade the appropriate area. ...

Which inequality is represented by the graph?

The inequality for the above graph is x ≥ 1. Inequalities in Two Variables from Graph. To find linear inequalities in two variables from graph, first we have to find two information from the graph. (i) Slope (ii) y -intercept. By using the above two information we can easily get a linear linear equation in the form y = mx + b.

How to graph inequalities?

Solve the equation algebraically, and plot it on the line with a dot on the answer. The dot should be open, with an arrow pointing toward the left.

What is the difference between an inequality and a graph?

The difference is that, since an inequality shows a set of values greater than or less than, your graph will show more than just a dot on a number line or a line on a coordinate plane. By using algebra and evaluating the inequality sign, you can determine which values are included in the solution of an inequality.

How to graph a line on a coordinate plane?

Graph the line on a coordinate plane. To do this, turn the inequality into an equation, and graph as you would any equation of a line. Plot the y-intercept, then use the slope to graph other points on the line.

How many variables should an inequality have?

Your inequality should only have one variable. If your inequality has two variables, it is more appropriate to graph it on a coordinate plane using another method.

What is a graph with no solution?

A graph of "no solution" would typically be two graph lines which never intersect.

How to solve inequality?

Solve for the variable. To solve the inequality isolate the variable using the same algebraic methods you would use to solve an equation. Remember that when you multiply or divide by a negative number, you need to flip the inequality sign.

Where should you shade in inequality?

you should shade in the area above the line. If the inequality shows

How to graph an inequality?

To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is ≤ or ≥, graph the equation as a solid line. This line divides the xy- plane into two regions: a region that satisfies the inequality, and a region that does not. Next, pick a point not on the line.

What can we use to graph a linear equation?

To graph a linear equation, we can use the slope and y-intercept.

Where is y on the equation?

Rearrange the equation so "y" is on the left and everything else on the right.

image
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version2.43sRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[03:59:07] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[03:59:07] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[03:59:07] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[03:59:07] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[03:59:07] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[03:59:07] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[03:59:07] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[03:59:07] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[03:59:07] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[03:59:07] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • Booting (15.43ms)
  • Application (2.41s)
  • 1 x Application (99.34%)
    2.41s
    1 x Booting (0.64%)
    15.43ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed2.39s
    • select * from `posts` where `published_at` <= '2025-06-07 03:59:07' and `slug` = 'how-do-you-write-an-inequality-for-a-graph' and `posts`.`deleted_at` is null limit 1
      3.92ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-07 03:59:07
      • 1. how-do-you-write-an-inequality-for-a-graph
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 148655 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      7.92msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 148655
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      1.49ms/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      660μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      770μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      2.37s/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 37219 limit 1
      820μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 37219
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        2W4pUN2vdQ4p9Sn19U4yHlZ1eQloKSN166EHXKyz
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/how-do-you-write-an-inequality-for-a-graph" ...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /how-do-you-write-an-inequality-for-a-graph
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:25 [ "cookie" => array:1 [ 0 => "_pk_id.64.7c30=bdff06681c83f7d6.1749248943.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InpKa1lwdEpNZUl5OUZkbGhpNlN1NHc9PSIsInZhbHVlIjoid1V0eEJRZzVlVWJYaHRrT1F2Y1A3Sjk5NE5yUUNtRHo2bERkeERxWUJLcXZvTjRwYjVheVNPU1VVVEI4cFFva2l1akFrZFQ0a01NWFVSckVHV0MxMHRRcnVmNGtJM3NNQTdYVDVULzBySUVCczU2UjUzK2FKRUpXdVdqcUI2NVUiLCJtYWMiOiJjNGM2ZTczYjZjYWVlNmE5NTU4MzdmYTVhYTg3ZGQwYWZlODU3MzE4NDUyMzEwYTZmZmQyMDAxYjViZDVhZDA2IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6InJKczAzZFQ3ek5OUG5pNHVqT016OVE9PSIsInZhbHVlIjoiS3hiVkhPQW5tUWRnb3ZOWkdCejBhcnFjMVBoSHJkRm10c2hEUWFkOHMwRXBMalkrZlNnMytQNEd3V3lsdjl0anlkZ2MvWVRkMm1YQXJpNWhqRi9PSjRURU5udkwzNEVMalRsVUlsTGQvUUl5SUFVTkZqYUlRaW9lMjVtcjVpSFUiLCJtYWMiOiI4ZjA2ODk4ODEyY2RmYmRmNDdjZWEzMGIxNDM2M2YwNTJhMzM2ZDZjMDQxNmZkOWI3ZGI1Y2ZhYmMzNWI2ZWFiIiwidGFnIjoiIn0%3D_pk_id.64.7c30=bdff06681c83f7d6.1749248943.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InpKa1lwdEpNZUl5OUZkbGhpNlN1NHc9PSIsInZhbHVlIjoid1V0eEJRZzVlVWJYaHRrT1F2Y1A3S" ] "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "216.73.216.213" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "cf-ray" => array:1 [ 0 => "94bb58c18fe0123d-ORD" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "216.73.216.213, 172.69.59.183" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:56 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/how-do-you-write-an-inequality-for-a-graph" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/how-do-you-write-an-inequality-for-a-graph" "REMOTE_PORT" => "39622" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.69.59.183" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_COOKIE" => "_pk_id.64.7c30=bdff06681c83f7d6.1749248943.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InpKa1lwdEpNZUl5OUZkbGhpNlN1NHc9PSIsInZhbHVlIjoid1V0eEJRZzVlVWJYaHRrT1F2Y1A3Sjk5NE5yUUNtRHo2bERkeERxWUJLcXZvTjRwYjVheVNPU1VVVEI4cFFva2l1akFrZFQ0a01NWFVSckVHV0MxMHRRcnVmNGtJM3NNQTdYVDVULzBySUVCczU2UjUzK2FKRUpXdVdqcUI2NVUiLCJtYWMiOiJjNGM2ZTczYjZjYWVlNmE5NTU4MzdmYTVhYTg3ZGQwYWZlODU3MzE4NDUyMzEwYTZmZmQyMDAxYjViZDVhZDA2IiwidGFnIjoiIn0%3D; askhelpdesk_session=eyJpdiI6InJKczAzZFQ3ek5OUG5pNHVqT016OVE9PSIsInZhbHVlIjoiS3hiVkhPQW5tUWRnb3ZOWkdCejBhcnFjMVBoSHJkRm10c2hEUWFkOHMwRXBMalkrZlNnMytQNEd3V3lsdjl0anlkZ2MvWVRkMm1YQXJpNWhqRi9PSjRURU5udkwzNEVMalRsVUlsTGQvUUl5SUFVTkZqYUlRaW9lMjVtcjVpSFUiLCJtYWMiOiI4ZjA2ODk4ODEyY2RmYmRmNDdjZWEzMGIxNDM2M2YwNTJhMzM2ZDZjMDQxNmZkOWI3ZGI1Y2ZhYmMzNWI2ZWFiIiwidGFnIjoiIn0%3D_pk_id.64.7c30=bdff06681c83f7d6.1749248943.; _pk_ses.64.7c30=1; XSRF-TOKEN=eyJpdiI6InpKa1lwdEpNZUl5OUZkbGhpNlN1NHc9PSIsInZhbHVlIjoid1V0eEJRZzVlVWJYaHRrT1F2Y1A3S" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "216.73.216.213" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_CF_RAY" => "94bb58c18fe0123d-ORD" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "216.73.216.213, 172.69.59.183" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1749248947.4668 "REQUEST_TIME" => 1749248947 ]
        request_cookies
        0 of 0
        array:4 [ "_pk_id_64_7c30" => null "_pk_ses_64_7c30" => null "XSRF-TOKEN" => "2W4pUN2vdQ4p9Sn19U4yHlZ1eQloKSN166EHXKyz" "askhelpdesk_session" => "mNlPfP3Ldhd9M1xfTbqUJALZ7nbgbcH4MYEAqEnE" ]
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Fri, 06 Jun 2025 22:29:07 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImJEbXAvZi90UjR3QmRJbHd1c3RtMXc9PSIsInZhbHVlIjoiZEhYUnFabk4yTFk4aFpudm9UY2gzcnpSZkd4Y3FnTGJGaWI3WGlGMGZVWlhMWHBaTnBLTFBlRWtabXhXSldRUnBNRkJDME0rbWdPai9jZXVUcXorNGxoVi9xRXdWLzhhZkY1Z3N1Qi83Nkxadk5vNGw3QU11ZGh3RG1SS0xxY0YiLCJtYWMiOiI0OTQxNjdlYTkyNzBiN2Q2OTVmNTBlZjM5ZDY0ZDhiNzQ1NGVhNzlmZmY2ZGUxMjFlMzg0Mzg0MDc2MWJmOGEyIiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 00:29:09 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6ImJEbXAvZi90UjR3QmRJbHd1c3RtMXc9PSIsInZhbHVlIjoiZEhYUnFabk4yTFk4aFpudm9UY2gzcnpSZkd4Y3FnTGJGaWI3WGlGMGZVWlhMWHBaTnBLTFBlRWtabXhXSldRUnBNRkJDM" 1 => "askhelpdesk_session=eyJpdiI6ImNXTUV2azN5M3I2aXhhNWc2ZUNVdmc9PSIsInZhbHVlIjoiNEZUQzRKQThwM0dYTVBPOHlTZFRMR2ZpbVhCa050U0Z2Y3JPaDRxZDI5RHhRNVR6S2JwOHpEeDc0cUU0MEJLb2grc2xidzFQSlE3Y1d0bHRpWU84MCtoR2pKU3I4UDdjYXpoYU5QVCtaSEwzWW1hY2l5YmQwcnBKMXZyR0NrOUoiLCJtYWMiOiIyMDcyODZkMjkwMDdiOWY3NjYyMDFkZGE0MWNlMjBmOTU0NTI2NDA1ZTRkZjQ1ZWM4YWU4MWJhMWVhYzNkYmM1IiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 00:29:09 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6ImNXTUV2azN5M3I2aXhhNWc2ZUNVdmc9PSIsInZhbHVlIjoiNEZUQzRKQThwM0dYTVBPOHlTZFRMR2ZpbVhCa050U0Z2Y3JPaDRxZDI5RHhRNVR6S2JwOHpEeDc0cUU0MEJL" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6ImJEbXAvZi90UjR3QmRJbHd1c3RtMXc9PSIsInZhbHVlIjoiZEhYUnFabk4yTFk4aFpudm9UY2gzcnpSZkd4Y3FnTGJGaWI3WGlGMGZVWlhMWHBaTnBLTFBlRWtabXhXSldRUnBNRkJDME0rbWdPai9jZXVUcXorNGxoVi9xRXdWLzhhZkY1Z3N1Qi83Nkxadk5vNGw3QU11ZGh3RG1SS0xxY0YiLCJtYWMiOiI0OTQxNjdlYTkyNzBiN2Q2OTVmNTBlZjM5ZDY0ZDhiNzQ1NGVhNzlmZmY2ZGUxMjFlMzg0Mzg0MDc2MWJmOGEyIiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 00:29:09 GMT; path=/XSRF-TOKEN=eyJpdiI6ImJEbXAvZi90UjR3QmRJbHd1c3RtMXc9PSIsInZhbHVlIjoiZEhYUnFabk4yTFk4aFpudm9UY2gzcnpSZkd4Y3FnTGJGaWI3WGlGMGZVWlhMWHBaTnBLTFBlRWtabXhXSldRUnBNRkJDM" 1 => "askhelpdesk_session=eyJpdiI6ImNXTUV2azN5M3I2aXhhNWc2ZUNVdmc9PSIsInZhbHVlIjoiNEZUQzRKQThwM0dYTVBPOHlTZFRMR2ZpbVhCa050U0Z2Y3JPaDRxZDI5RHhRNVR6S2JwOHpEeDc0cUU0MEJLb2grc2xidzFQSlE3Y1d0bHRpWU84MCtoR2pKU3I4UDdjYXpoYU5QVCtaSEwzWW1hY2l5YmQwcnBKMXZyR0NrOUoiLCJtYWMiOiIyMDcyODZkMjkwMDdiOWY3NjYyMDFkZGE0MWNlMjBmOTU0NTI2NDA1ZTRkZjQ1ZWM4YWU4MWJhMWVhYzNkYmM1IiwidGFnIjoiIn0%3D; expires=Sat, 07-Jun-2025 00:29:09 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6ImNXTUV2azN5M3I2aXhhNWc2ZUNVdmc9PSIsInZhbHVlIjoiNEZUQzRKQThwM0dYTVBPOHlTZFRMR2ZpbVhCa050U0Z2Y3JPaDRxZDI5RHhRNVR6S2JwOHpEeDc0cUU0MEJL" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "2W4pUN2vdQ4p9Sn19U4yHlZ1eQloKSN166EHXKyz" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/how-do-you-write-an-inequality-for-a-graph" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]