Introduction to Plotting Lines on the Rectangular Coordinate System

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

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

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

Solution: $x=-4$

If you missed this problem, review this example.

Name the ordered pair of each point shown: The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point

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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 $\left(0,1\right)$ .

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. $\left(-4,3\right)$

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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.

(0, 2)

$\left(0,2\right)$

(2, - 4)

$\left(2,-4\right)$

(- 4, 3)

$\left(-4,3\right)$

x = 0, y = 2

$x=\color{blue}{0}, y=\color{red}{2}$

$x+4y=8$

$\color{blue}{0}+4\cdot\color{red}{2}\stackrel{?}{=}8$

$0+8\stackrel{?}{=}8$

$8=8\checkmark$

x = 2, y = - 4

$x=\color{blue}{2}, y=\color{red}{-4}$

$x+4y=8$

$\color{blue}{2}+4(\color{red}{-4})\stackrel{?}{=}8$

$2+(-16)\stackrel{?}{=}8$

$-14\not=8$

x = - 4, y = 3

$x=\color{blue}{-4}, y=\color{red}{3}$

$x+4y=8$

$\color{blue}{-4}+4\cdot\color{red}{3}\stackrel{?}{=}8$

$-4+12\stackrel{?}{=}8$

$8=8\checkmark$

(0, 2)

$\left(0,2\right)$ is a solution.

(2, - 4)

$\left(2,-4\right)$ is not a solution.

(- 4, 3)

$\left(-4,3\right)$ is a solution.