Answer
$x=2$, $y=-6$. See graph below.
Work Step by Step
The slope-intercept form of a line is given by $y=mx+b$
Now, rewrite the given equation of the line in slope-intercept form as below:
$\begin{align}
& 6x-2y-12=0 \\
& 2y=6x-12 \\
& y=3x-6
\end{align}$
To find the value of the slope m and y intercept b, we will compare both equations:
$\begin{align}
& m=3 \\
& b=-6 \\
\end{align}$
Hence, the slope of the provided equation is $3$ and the $y-\text{intercept}$ is −6.
Now,
Consider the slope–intercept form above, that is
$y=3x-6$
To plot the equation on the graph, follow the steps given below:
Step 1: Plot the $y-\text{intercept}$ on the $y\ \text{axis}$, that is the point $\left( 0,-6 \right)$.
Step 2: Write slope $m$ in fraction, that is $\frac{3}{1}$.
Step 3: Plot the second point on the line passing through $\left( 0,-6 \right)$. Based on the slope, move 3 units up and 1 units right. The second point is $\left( 1,-3 \right)$.
The resulting graph is shown below.
