What you’ll learn to do: Plot lines on the rectangular coordinate system using x- and y-intercepts

One of the easiest ways to graph a line is by using the x- and y- intercepts as two of your points.

In this section, we will learn how to:

• Identify the x- and y-intercepts on a graph and as ordered pairs
• Find the intercepts from an equation of a line
• Graph a linear equation using x and y-intercepts

Before you get started in this module, try a few practice problems and review prior concepts.

readiness quiz

1)

Solve: [latex]3x+4y=-12[/latex] for [latex]x[/latex] when [latex]y=0[/latex].

Solution: [latex]x=-4[/latex]

2)

If you missed this problem, review this example.

Name the ordered pair of each point shown:

Show Solution

Solution

Point A is on the x-axis at [latex]x=-4[/latex] .	The coordinates of point A are [latex]\left(-4,0\right)[/latex] .
Point B is on the y-axis at [latex]y=-2[/latex]	The coordinates of point B are [latex]\left(0,-2\right)[/latex] .
Point C is on the x-axis at [latex]x=3[/latex] .	The coordinates of point C are [latex]\left(3,0\right)[/latex] .
Point D is on the y-axis at [latex]y=1[/latex] .	The coordinates of point D are [latex]\left(0,1\right)[/latex] .

3)

If you missed this problem, review the example below.

Determine which ordered pairs are solutions of the equation [latex]x+4y=8\text{:}[/latex]

1. [latex]\left(0,2\right)[/latex]
2. [latex]\left(2,-4\right)[/latex]
3. [latex]\left(-4,3\right)[/latex]

Show Solution

Solution
Substitute the [latex]x\text{- and}y\text{-values}[/latex] from each ordered pair into the equation and determine if the result is a true statement.

1. [latex]\left(0,2\right)[/latex]	2. [latex]\left(2,-4\right)[/latex]	3. [latex]\left(-4,3\right)[/latex]
[latex]x=\color{blue}{0}, y=\color{red}{2}[/latex] [latex]x+4y=8[/latex] [latex]\color{blue}{0}+4\cdot\color{red}{2}\stackrel{?}{=}8[/latex] [latex]0+8\stackrel{?}{=}8[/latex] [latex]8=8\checkmark[/latex]	[latex]x=\color{blue}{2}, y=\color{red}{-4}[/latex] [latex]x+4y=8[/latex] [latex]\color{blue}{2}+4(\color{red}{-4})\stackrel{?}{=}8[/latex] [latex]2+(-16)\stackrel{?}{=}8[/latex] [latex]-14\not=8[/latex]	[latex]x=\color{blue}{-4}, y=\color{red}{3}[/latex] [latex]x+4y=8[/latex] [latex]\color{blue}{-4}+4\cdot\color{red}{3}\stackrel{?}{=}8[/latex] [latex]-4+12\stackrel{?}{=}8[/latex] [latex]8=8\checkmark[/latex]
[latex]\left(0,2\right)[/latex] is a solution.	[latex]\left(2,-4\right)[/latex] is not a solution.	[latex]\left(-4,3\right)[/latex] is a solution.