To solve the given system of linear equations and find the intercepts step-by-step, we need to determine the x-intercept and y-intercept for the equations [tex]\(4x - 2y = 8\)[/tex] and [tex]\( y = \frac{3}{2}x - 2\)[/tex].
### Step 1: Plot the [tex]\(x\)[/tex]-intercept of the first equation.
For the x-intercept, set [tex]\(y = 0\)[/tex] in the first equation:
[tex]\[ 4x - 2(0) = 8 \][/tex]
[tex]\[ 4x = 8 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the x-intercept of the first equation is [tex]\((2, 0)\)[/tex].
### Step 2: Plot the [tex]\(y\)[/tex]-intercept of the first equation.
For the y-intercept, set [tex]\(x = 0\)[/tex] in the first equation:
[tex]\[ 4(0) - 2y = 8 \][/tex]
[tex]\[ -2y = 8 \][/tex]
[tex]\[ y = -4 \][/tex]
So, the y-intercept of the first equation is [tex]\((0, -4)\)[/tex].
### Step 3: Plot the [tex]\(y\)[/tex]-intercept of the second equation.
For the y-intercept, set [tex]\(x = 0\)[/tex] in the second equation:
[tex]\[ y = \frac{3}{2}(0) - 2 \][/tex]
[tex]\[ y = -2 \][/tex]
So, the y-intercept of the second equation is [tex]\((0, -2)\)[/tex].
### Summary of the Intercepts
Based on the steps above, the correct intercept points are:
1. [tex]\(x\)[/tex]-intercept of the first equation: [tex]\((2, 0)\)[/tex]
2. [tex]\(y\)[/tex]-intercept of the first equation: [tex]\((0, -4)\)[/tex]
3. [tex]\(y\)[/tex]-intercept of the second equation: [tex]\((0, -2)\)[/tex]
Thus, the points are:
[tex]\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
0 & -4 \\
2 & 0 \\
0 & -2 \\
\hline
\end{array}
\][/tex]
