Answer
$x=-3/2$, $y=-6$, see graph
Work Step by Step
Consider the given linear equation
$8x-2y+12=0$
Use intercepts to graph the given equation as follows:
Step 1: Find the $x$ intercept.
To calculate the x intercept of the line, substitute $y=0$ in the equation and find the value of x.
$\begin{align}
& 8x-2\times 0+12=0 \\
& 8x=-12 \\
& x=\frac{\left( -12 \right)}{8} \\
& =-1.5
\end{align}$
So, the $x$ intercept of the given equation $8x-2y+12=0$ is $-1.5$. Hence, the line passes through the point $\left( -1.5,0 \right)$.
Step 2: Find the $y$ intercept.
To calculate the y intercept of the line, substitute $x=0$ in the equation and find the value of y.
$\begin{align}
& 8\times 0-2y+12=0 \\
& -2y=-12 \\
& y=\frac{\left( -12 \right)}{\left( -2 \right)} \\
& =6
\end{align}$
So, the $y$ intercept of the equation $8x-2y+12=0$ is 6. Hence, the line passes through the point $\left( 0,6 \right)$.
Step 3: Plot the graph the equation of the straight line.
Locate the two intercepts $\left( -1.5,0 \right)$ and $\left( 0,6 \right)$. Connect them by a straight line.
The graph of the given equation $8x-2y+12=0$ is as follows:
