Intermediate Algebra, Chapter 3, 3.1, Section 3.1, Problem 56

Determine the $x$- and $y$-intercepts. Then graph the equation $\displaystyle - \frac{9}{4}y = x$.

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


$\begin{equation} \begin{aligned} - \frac{9}{4} (0) =& x \\ \\ 0 =& x \end{aligned} \end{equation}$


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


$\begin{equation} \begin{aligned} - \frac{9}{4} y =& 0 \\ \\ y =& 0 \end{aligned} \end{equation}$


Both intercepts are the same point, $(0,0)$ which means that the graph passes through the origin. To find another point, choose any nonzero number for $x$ or $y$ and solve for the other variable. We choose $x = -9$.


$\begin{equation} \begin{aligned} - \frac{9}{4}y =& x \\ \\ - \frac{9}{4} y =& -9 \\ \\ y =& -9 \left( - \frac{4}{9} \right) \\ \\ y =& 4 \end{aligned} \end{equation}$


This gives to ordered pair $(-9,4)$. So the graph is