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