Intermediate Algebra, Chapter 3, 3.1, Section 3.1, Problem 42

Determine the $x$- and $y$-intercepts. Then graph the equation $\displaystyle \frac{5}{7}x + \frac{6}{7}y = -2$.

To find $x$-intercept, we set $y = 0$


$\begin{equation} \begin{aligned} \frac{5}{7}x + \frac{6}{7}(0) =& -2 \\ \\ \frac{5}{7}x =& -2 \\ \\ x =& -2 \left( \frac{7}{5} \right) \\ \\ x =& - \frac{14}{5} \end{aligned} \end{equation}$


To find $y$-intercept, we set $x = 0$


$\begin{equation} \begin{aligned} \frac{5}{7}(0) + \frac{6}{7} y \\ \\ \frac{6}{7}y =& -2 \\ \\ y =& -2 \left( \frac{7}{6} \right) \\ \\ y =& - \frac{7}{3} \end{aligned} \end{equation}$


The line $\displaystyle \frac{5}{7}x + \frac{6}{7}y = -2$ passes through the points $\displaystyle \left( - \frac{14}{5}, 0 \right)$ and $\displaystyle \left( 0, - \frac{7}{3} \right)$. So the graph is