Graph Linear Equations in Two Variables: example 4.15

Graph the equation $2 x - 3 y = 6$ .

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.

Your turn

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

Graph the equation $4 x + 2 y = 8$ .

How did it go?

Find three points that are solutions to the equation.	$\begin{matrix} 2 x - 3 y & = & 6 \end{matrix}$
First, let $x = 0$ .	$\begin{matrix} 2 (0) - 3 y & = & 6 \end{matrix}$
Solve for $y$ .	$\begin{matrix} −3 y & = & 6 \\ y & = & −2 \end{matrix}$
Now let $y = 0$ .	$\begin{matrix} 2 x - 3 (0) & = & 6 \end{matrix}$
Solve for $x$ .	$\begin{matrix} 2 x & = & 6 \\ x & = & 3 \end{matrix}$
We need a third point. Remember, we can choose any value for $x$ or $y$ . We'll let $x = 6$ .	$\begin{matrix} 2 (6) - 3 y & = & 6 \end{matrix}$
Solve for $y$ .	$\begin{matrix} 12 - 3 y & = & 6 \\ −3 y & = & −6 \\ y & = & 2 \end{matrix}$

Find three points that are solutions to the equation.	$\begin{matrix} 2 x - 3 y & = & 6 \end{matrix}$
First, let $x = 0$ .	$\begin{matrix} 2 (0) - 3 y & = & 6 \end{matrix}$
Solve for $y$ .	$\begin{matrix} −3 y & = & 6 \\ y & = & −2 \end{matrix}$
Now let $y = 0$ .	$\begin{matrix} 2 x - 3 (0) & = & 6 \end{matrix}$
Solve for $x$ .	$\begin{matrix} 2 x & = & 6 \\ x & = & 3 \end{matrix}$
We need a third point. Remember, we can choose any value for $x$ or $y$ . We'll let $x = 6$ .	$\begin{matrix} 2 (6) - 3 y & = & 6 \end{matrix}$
Solve for $y$ .	$\begin{matrix} 12 - 3 y & = & 6 \\ −3 y & = & −6 \\ y & = & 2 \end{matrix}$