Intermediate Algebra, Chapter 3, 3.1, Section 3.1, Problem 54

Determine the $x$- and $y$-intercepts. Then graph the equation $4y = 3x$.

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


$
\begin{equation}
\begin{aligned}

4(0) =& 3x \\
0 =& 3x \\
0 =& x

\end{aligned}
\end{equation}
$


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


$
\begin{equation}
\begin{aligned}

4y =& 3(0) \\
4y =& 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 $x = 4$.


$
\begin{equation}
\begin{aligned}

4y =& 3x \\
4y =& 3(4) \\
4y =& 12 \\
y =& 3

\end{aligned}
\end{equation}
$


This gives to ordered pair $(4,3)$. So the graph is