1.5.2 Graphing Linear Functions in Two Variables

Example

Graph $3x-6y=18$ using the intercepts, then identify key characteristics.

Step 1 - Find the $x$-intercept.
To find the $x$-intercept, let $y=0$.

$\begin{array}{ccc}\hfill 3x-6y& \hfill =\hfill & 18\hfill \\ \hfill 3x-6(0)& \hfill =\hfill & 18\hfill \\ \hfill 3x& \hfill =\hfill & 18\hfill \\ \hfill x& \hfill =\hfill & 6\hfill \end{array}$

$(6,0)$ is the $x$-intercept
The $x$-intercept is also called a solution or zero.

Step 2 -Find the $y$-intercept.
To find the $y$-intercept, let $x=0$.

$\begin{array}{ccc}\hfill 3x-6y& \hfill =\hfill & 18\hfill \\ \hfill 3(0)-6y& \hfill =\hfill & 18\hfill \\ \hfill -6y& \hfill =\hfill & 18\hfill \\ \hfill y& \hfill =\hfill & -3\hfill \end{array}$

$(0,-3)$ is the $y$-intercept

Step 3 -Graph the line by connecting the $y$-intercepts.

Step 4 - Find the slope of the line.

$\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}=\frac{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}{\mathrm{r}\mathrm{u}\mathrm{n}}=\frac{3}{6}=\frac{1}{2}$