Example 11.26 from Prealgebra, 11.3 Graphing with Intercepts

Graphing with Intercepts: example 11.26

Graph $- x + 2 y = 6$ using intercepts.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, find the $x -intercept .$ Let $y = 0,$

$\begin{matrix} - x + 2 y = 6 \\ - x + 2 (0) = 6 \\ - x = 6 \\ x = −6 \end{matrix}$

The $x -intercept$ is $(- 6, 0).$

Now find the $y -intercept .$ Let $x = 0 .$

$\begin{matrix} - x + 2 y = 6 \\ −0 + 2 y = 6 \\ 2 y = 6 \\ y = 3 \end{matrix}$

The $y -intercept$ is $(0, 3).$

Find a third point. We’ll use $x = 2,$

$\begin{matrix} - x + 2 y = 6 \\ −2 + 2 y = 6 \\ 2 y = 8 \\ y = 4 \end{matrix}$

A third solution to the equation is $(2, 4).$

Summarize the three points in a table and then plot them on a graph.

$- x + 2 y = 6$

x y (x,y)

$x −2 y = 4 .$ $0$ $(−6, 0)$

$0$ $3$ $(0, 3)$

$2$ $4$ $(2, 4)$

Do the points line up? Yes, so draw line through the points.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Graph the line using the intercepts: $x −2 y = 4 .$

How did it go?