Answer
The graph is shown in the image file.
Work Step by Step
The given linear function is
$\Rightarrow 3x-4f(x)=6$
For the $x-$intercept.
Let $f(x)=0$ and solve for $x$.
$\Rightarrow 3x-4(0)=6$
$\Rightarrow 3x-0=6$
$\Rightarrow 3x=6$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}=\frac{6}{3}$
Simplify.
$\Rightarrow x=2$
The $x-$intercept is $2$, so the line passes through $(2,0)$.
For the $y-$intercept.
Let $x=0$ and solve for $f(x)$.
$\Rightarrow 3(0)-4f(0)=6$
$\Rightarrow 0-4f(0)=6$
$\Rightarrow -4f(0)=6$
Divide both sides by $-4$.
$\Rightarrow \frac{-4f(0)}{-4}=\frac{6}{-4}$
$\Rightarrow f(0)=-\frac{3}{2}$
The $y-$intercept is $-\frac{3}{2}$, so the line passes through $\left
(0,-\frac{3}{2} \right)$
Let $x=-2$ and solve for $f(x)$
$\Rightarrow 3(-2)-4f(-2)=6$
$\Rightarrow -6-4f(-2)=6$
$\Rightarrow -6-4f(-2)+6=6+6$
$\Rightarrow -4f(-2)=12$
Divide both sides by $-4$.
$\Rightarrow \frac{-4f(-2)}{-4}=\frac{12}{-4}$
$\Rightarrow f(-2)=-3$
The checkpoint is $\left (-2,-3 \right)$.
Draw a line through the three points.
