Question

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

Explanation:

Step1: Rewrite 2nd equation in slope-intercept form

Rearrange $x - y = 8$ to solve for $y$:
$y = x - 8$

Step2: Find points for first line

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

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

Step3: Find points for second line

For $y = x - 8$:

• When $x=0$, $y = 0 - 8 = -8$ → Point $(0, -8)$
• When $x=8$, $y = 8 - 8 = 0$ → Point $(8, 0)$

Step4: Find intersection algebraically

Set equations equal:
$-\frac{3}{2}x - 3 = x - 8$
Multiply all terms by 2 to eliminate fraction:
$-3x - 6 = 2x - 16$
Solve for $x$:
$-3x - 2x = -16 + 6$
$-5x = -10$
$x = 2$
Substitute $x=2$ into $y = x - 8$:
$y = 2 - 8 = -6$

Answer:

The solution (intersection point) is $(2, -6)$
To plot:

1. For $y = -\frac{3}{2}x - 3$, plot $(0, -3)$ and $(2, -6)$, then draw the line through them.
2. For $y = x - 8$, plot $(0, -8)$ and $(8, 0)$, then draw the line through them. The lines cross at $(2, -6)$.