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