Answer
Graph of $y=\dfrac{2}{3}x+4$
Work Step by Step
The $x-$intercept is the value of $x$ when $y=0.$ Setting $y=0,$ the $x$-intercept of the given equation, $
y=\dfrac{2}{3}x+4
,$ is
\begin{align*}
0&=\dfrac{2}{3}x+4
\\\\
0-4&=\dfrac{2}{3}x+4-4
\\\\
-4&=\dfrac{2}{3}x
\\\\
\left(\dfrac{3}{2}\right)(-4)&=\left(\dfrac{2}{3}x\right)\left(\dfrac{3}{2}\right)
\\\\
-6&=x
.\end{align*} The $x$-intercept is $ \left( -6,0 \right) $.
The $y-$intercept is the value of $y$ when $x=0.$ Setting $x=0,$ the $y$-intercept of the given equation is
\begin{align*}
y&=\dfrac{2}{3}(0)+4
\\\\
y&=0+4
\\
y&=4
.\end{align*}
The $y$-intercept is $ (0,4) $.
By connecting the intercepts, the graph of the given equation is determined.
