Answer
The graph is shown below.
Work Step by Step
The given linear equation is
$\Rightarrow 3x-5y=15$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow 3x-5(0)=15$
$\Rightarrow 3x=15$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}=\frac{15}{3}$
$\Rightarrow x=5$
The $x−$intercept is $5$, so the line passes through $(5,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow 3(0)-5y=15$
$\Rightarrow -5y=15$
Divide both sides by $-5$.
$\Rightarrow \frac{-5y}{-5}=\frac{15}{-5}$
Simplify.
$\Rightarrow y=-3$
The $y−$intercept is $-3$, so the line passes through $(0,-3)$.
Checkpoint plug $y=3$.
$\Rightarrow 3x-5(3)=15$
$\Rightarrow 3x-15=15$
Add $15$ to both sides.
$\Rightarrow 3x-15+15=15+15$
$\Rightarrow 3x=30$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}=\frac{30}{3}$
$\Rightarrow x=10$
The checkpoint is $(10,3)$.
Draw a straight line through these three points.
