Answer
The graph of the provided linear function is shown below:
Work Step by Step
Step1: Find the value of the $x-\text{intercept}$
Let $f\left( x \right)=0$
Substitute the value of $f\left( x \right)$ in the given linear function
$\begin{align}
& 3x-4\times \left( 0 \right)-6=0\text{ } \\
& 3x-6+6=+6\text{ }\left( \text{adding 6 to both side} \right) \\
& \frac{3x}{3}=\frac{6}{3}\text{ }\left( \text{dividing both side by 3} \right) \\
& x=2
\end{align}$
Hence, the value of the x-intercept is $2$.
Or, in coordinate form, the point found is $\left( 2,0 \right)$
Step 2: Find the value of the $y-\text{intercept}$
Let $x=0$
Substitute the value of $x$ in the provided linear function
$\begin{align}
& 3\left( 0 \right)-4f\left( x \right)-6=0\text{ } \\
& -4f\left( x \right)-6+6=+6\text{ }\left( \text{adding 6 to both side} \right) \\
& -\frac{4f\left( x \right)}{-4}=\frac{6}{-4}\text{ }\left( \text{dividing both side by}-\text{ 4} \right) \\
& f\left( x \right)=-\frac{3}{2}
\end{align}$
Hence, the value of the $y-\text{intercept}$ is $-\frac{3}{2}$.
Or,
In coordinate form, the point found is $\left( 0,-\frac{3}{2} \right)$
With the help of the $x$ and $y$ intercepts, the graph of the provided linear function can be plotted.
