Answer
graph of $5x-4y=3$:
Work Step by Step
The $x$-intercept is the value of $x$ when $y=0.$ Setting $y=0$ in the given equation, $
5x-4y=3
,$ results to
\begin{align*}
5x-4(0)&=3
\\
5x-0&=3
\\
5x&=3
\\\\
\dfrac{5x}{5}&=\dfrac{3}{5}
\\\\
x&=\dfrac{3}{5}
.\end{align*}
Hence, the $x$-intercept is $\left(
\dfrac{3}{5},0
\right)$.
The $y$-intercept is the value of $y$ when $x=0.$ Setting $x=0$ in the given equation results to
\begin{align*}
5(0)-4y&=3
\\
0-4y&=3
\\
-4y&=3
\\\\
\dfrac{-4y}{-4}&=\dfrac{3}{-4}
\\\\
y&=-\dfrac{3}{4}
.\end{align*}
Hence, the $y$-intercept is $\left(
0,-\dfrac{3}{4}
\right)$.
By connecting the two intercepts, the graph of the given line is determined.