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: $3x+4y=-12$ for $x$ when $y=0$.

Solution: $x=-4$

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

3)

If you missed this problem, review the example below.

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

1. $\left(0,2\right)$
2. $\left(2,-4\right)$
3. $\left(-4,3\right)$

Show Solution

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

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