{"id":1732,"date":"2024-06-05T20:59:13","date_gmt":"2024-06-05T20:59:13","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&p=1732"},"modified":"2025-08-13T23:25:30","modified_gmt":"2025-08-13T23:25:30","slug":"graphs-of-linear-functions-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/graphs-of-linear-functions-learn-it-2\/","title":{"raw":"Graphs of Linear Functions: Learn It 2","rendered":"Graphs of Linear Functions: Learn It 2"},"content":{"raw":"

Describing Horizontal and Vertical Lines<\/h2>\r\nThere are two special cases of lines on a graph\u2014horizontal and vertical lines.\r\n\r\nA horizontal line<\/strong> is a line defined by an equation of the form [latex]f\\left(x\\right)=b[\/latex] where [latex]b[\/latex] is a constant. A horizontal line indicates a constant output or [latex]y[\/latex]-value.\r\n\r\n
In the graph and table, we see that the output has a value of [latex]2[\/latex] for every input value. The change in outputs between any two points is [latex]0[\/latex]. In the slope formula, the numerator is [latex]0[\/latex], so the slope is [latex]0[\/latex].If we use [latex]m = 0[\/latex] in the equation [latex]f(x)=mx+b[\/latex], the equation simplifies to [latex]f(x)=b[\/latex].\r\n[latex]\\\\[\/latex]\r\nIn other words, the value of the function is a constant. This graph represents the function [latex]f(x)=2[\/latex].\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]\"\" Graph of a line with box of x and y values[\/caption]\r\n\r\n<\/section>A vertical line<\/strong> is a line defined by an equation of the form [latex]x=a[\/latex] where [latex]a[\/latex] is a constant. A vertical line indicates a constant input or [latex]x[\/latex]-value.\r\n\r\n
\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]\"\" Graph of a line with box of x and y values[\/caption]\r\n\r\nWe can see that the input value for every point on the line is [latex]2[\/latex], but the output value varies. Because this input value is mapped to more than one output value, a vertical line does not<\/strong> represent a function<\/strong>. Notice that between any two points, the change in the input values is zero. In the slope formula, the denominator will be zero, so the slope of a vertical line is undefined.\"MNotice that a vertical line has an [latex]x[\/latex]-intercept but no [latex]y[\/latex]-<\/em>intercept unless it\u2019s the line [latex]x= 0[\/latex]. This graph represents the line [latex]x= 2[\/latex].<\/section>
\r\n

horizontal and vertical lines<\/h3>\r\nLines can be horizontal or vertical.\r\n
    \r\n \t
  • A horizontal line<\/strong> is a line defined by an equation of the form [latex]f\\left(x\\right)=b[\/latex] where [latex]b[\/latex] is a constant.<\/li>\r\n \t
  • A vertical line<\/strong> is a line defined by an equation of the form [latex]x=a[\/latex] where [latex]a[\/latex] is a constant.<\/li>\r\n<\/ul>\r\n<\/section>
    Write the equation of the line graphed below.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"300\"]\"Graph Graph of a line[\/caption]\r\n\r\n[reveal-answer q=\"365304\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"365304\"]For any [latex]x[\/latex]-value, the [latex]y[\/latex]-value is [latex]\u20134[\/latex], so the equation is [latex]y=\u20134[\/latex].[\/hidden-answer]<\/section>
    [ohm2_question hide_question_numbers=1]19209[\/ohm2_question]<\/section><\/section>
    Write the equation of the line graphed below.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"300\"]\"Graph Graph of a line[\/caption]\r\n\r\n[reveal-answer q=\"178822\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"178822\"]The constant [latex]x[\/latex]-value is [latex]7[\/latex], so the equation is [latex]x=7[\/latex].[\/hidden-answer]<\/section>
    [ohm_question hide_question_numbers=1]290352[\/ohm_question]<\/section><\/section>","rendered":"

    Describing Horizontal and Vertical Lines<\/h2>\n

    There are two special cases of lines on a graph\u2014horizontal and vertical lines.<\/p>\n

    A horizontal line<\/strong> is a line defined by an equation of the form [latex]f\\left(x\\right)=b[\/latex] where [latex]b[\/latex] is a constant. A horizontal line indicates a constant output or [latex]y[\/latex]-value.<\/p>\n

    In the graph and table, we see that the output has a value of [latex]2[\/latex] for every input value. The change in outputs between any two points is [latex]0[\/latex]. In the slope formula, the numerator is [latex]0[\/latex], so the slope is [latex]0[\/latex].If we use [latex]m = 0[\/latex] in the equation [latex]f(x)=mx+b[\/latex], the equation simplifies to [latex]f(x)=b[\/latex].
    \n[latex]\\\\[\/latex]
    \nIn other words, the value of the function is a constant. This graph represents the function [latex]f(x)=2[\/latex].<\/p>\n
    \"\"
    Graph of a line with box of x and y values<\/figcaption><\/figure>\n<\/section>\n

    A vertical line<\/strong> is a line defined by an equation of the form [latex]x=a[\/latex] where [latex]a[\/latex] is a constant. A vertical line indicates a constant input or [latex]x[\/latex]-value.<\/p>\n

    \n
    \"\"
    Graph of a line with box of x and y values<\/figcaption><\/figure>\n

    We can see that the input value for every point on the line is [latex]2[\/latex], but the output value varies. Because this input value is mapped to more than one output value, a vertical line does not<\/strong> represent a function<\/strong>. Notice that between any two points, the change in the input values is zero. In the slope formula, the denominator will be zero, so the slope of a vertical line is undefined.\"MNotice that a vertical line has an [latex]x[\/latex]-intercept but no [latex]y[\/latex]–<\/em>intercept unless it\u2019s the line [latex]x= 0[\/latex]. This graph represents the line [latex]x= 2[\/latex].<\/section>\n

    \n

    horizontal and vertical lines<\/h3>\n

    Lines can be horizontal or vertical.<\/p>\n

      \n
    • A horizontal line<\/strong> is a line defined by an equation of the form [latex]f\\left(x\\right)=b[\/latex] where [latex]b[\/latex] is a constant.<\/li>\n
    • A vertical line<\/strong> is a line defined by an equation of the form [latex]x=a[\/latex] where [latex]a[\/latex] is a constant.<\/li>\n<\/ul>\n<\/section>\n
      Write the equation of the line graphed below.<\/p>\n
      \"Graph
      Graph of a line<\/figcaption><\/figure>\n