#### Answer

$x\text{-intercept: }
\left( \dfrac{28}{5},0 \right)
\\y\text{-intercept: }
(0,4)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of intercepts to find the $x$- and $y$-intercepts of the given equation, $
5x+7y=28
.$ Then plot the points corresponding to the intercepts and connect these with a line to get the graph.
$\bf{\text{Solution Details:}}$
The $x$-intercept is the value of $x$ when $y=0.$ Substituting $y=0$ in the given equation, then
\begin{array}{l}\require{cancel}
5x+7y=28
\\\\
5x+7(0)=28
\\\\
5x+0=28
\\\\
5x=28
\\\\
x=\dfrac{28}{5}
.\end{array}
Hence, the $x$-intercept is $
\left( \dfrac{28}{5},0 \right)
.$
The $y$-intercept is the value of $y$ when $x=0.$ Substituting $x=0$ in the given equation, then
\begin{array}{l}\require{cancel}
5(0)+7y=28
\\\\
0+7y=28
\\\\
7y=28
\\\\
y=\dfrac{28}{7}
\\\\
y=4
.\end{array}
Hence, the $y$-intercept is $
(0,4)
.$
Connecting the following intercepts,
\begin{array}{l}\require{cancel}
x\text{-intercept: }
\left( \dfrac{28}{5},0 \right)
\\y\text{-intercept: }
(0,4)
,\end{array}
gives the graph of the given equation.