Example 11.19 from Prealgebra, 11.2 Graphing Linear Equations

Graphing Linear Equations: example 11.19

Graph the equation $3 x + y = −1 .$

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
Find three points that are solutions to the equation.

First, solve the equation for $y .$

$\begin{matrix} 3 x + y & = & −1 \\ y & = & −3 x - 1 \end{matrix}$
We’ll let $x$ be $0, 1,$ and $−1$ to find three points. The ordered pairs are shown in the table. Plot the points, check that they line up, and draw the line.

$y = −3 x - 1$

$x$ $y$ $(x, y)$

$0$ $−1$ $2 x + y = 2 .$

$1$ $−4$ $(1, −4)$

$−1$ $2$ $(−1, 2)$

If you can choose any three points to graph a line, how will you know if your graph matches the one shown in the answers in the book? If the points where the graphs cross the $x -$ and $y$ -axes are the same, the graphs match.

Your turn

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

Graph each equation: $2 x + y = 2 .$

How did it go?