Question

solve the following system of equations graphically on the set of axes below.
$y = -\frac{3}{2}x - 8$
$x - 2y = 8$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

Rearrange $x-2y=8$ to $y=mx+b$ form:

$$\begin{align*} -2y&=-x+8\\ y&=\frac{1}{2}x-4 \end{align*}$$

Step2: Find points for first line

For $y=-\frac{3}{2}x-8$:

• When $x=0$, $y=-8$ → Point $(0, -8)$
• When $x=-4$, $y=-\frac{3}{2}(-4)-8=6-8=-2$ → Point $(-4, -2)$

Step3: Find points for second line

For $y=\frac{1}{2}x-4$:

• When $x=0$, $y=-4$ → Point $(0, -4)$
• When $x=8$, $y=\frac{1}{2}(8)-4=4-4=0$ → Point $(8, 0)$

Step4: Find intersection algebraically

Set equations equal:

$$\begin{align*} -\frac{3}{2}x-8&=\frac{1}{2}x-4\\ -3x-16&=x-8\\ -4x&=8\\ x&=-2 \end{align*}$$

Substitute $x=-2$ into $y=\frac{1}{2}x-4$:

$$ y=\frac{1}{2}(-2)-4=-1-4=-5 $$

Answer:

The solution (intersection point) is $\boldsymbol{(-2, -5)}$.
To plot the lines:

1. For $y=-\frac{3}{2}x-8$: plot $(0, -8)$ and $(-4, -2)$, then draw the line through them.
2. For $x-2y=8$ (or $y=\frac{1}{2}x-4$): plot $(0, -4)$ and $(8, 0)$, then draw the line through them.