Question

solve the following system of equations graphically on the set of axes below.
$y = -dfrac{3}{2}x - 2$
$y = dfrac{1}{2}x + 6$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection algebraically

Set equations equal:
$$-\frac{3}{2}x - 2 = \frac{1}{2}x + 6$$

Step2: Solve for x

Multiply by 2, simplify:
$$-3x - 4 = x + 12$$
$$-4x = 16$$
$$x = -4$$

Step3: Find y with x=-4

Substitute into second equation:
$$y = \frac{1}{2}(-4) + 6 = -2 + 6 = 4$$

Step4: Identify line points (Line1)

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

• y-intercept: $(0, -2)$
• When $x=2$, $y=-\frac{3}{2}(2)-2=-5$, so $(2, -5)$

Step5: Identify line points (Line2)

For $y=\frac{1}{2}x+6$:

• y-intercept: $(0, 6)$
• When $x=2$, $y=\frac{1}{2}(2)+6=7$, so $(2, 7)$

Answer:

The solution to the system is $(-4, 4)$. To graph:

1. For $y=-\frac{3}{2}x-2$, plot $(0, -2)$ and $(2, -5)$, then draw the line through them.
2. For $y=\frac{1}{2}x+6$, plot $(0, 6)$ and $(2, 7)$, then draw the line through them.

The two lines intersect at $(-4, 4)$.