Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{3}x + 5$
$y = -2x - 2$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection algebraically

Set equations equal: $\frac{1}{3}x + 5 = -2x - 2$

Step2: Solve for x

Multiply by 3: $x + 15 = -6x - 6$
$x + 6x = -6 - 15$
$7x = -21$
$x = -3$

Step3: Find y-value

Substitute $x=-3$ into $y=-2x-2$:
$y = -2(-3) - 2 = 6 - 2 = 4$

Step4: Graph first line ($y=\frac{1}{3}x+5$)

• y-intercept: $(0,5)$
• Second point: when $x=3$, $y=\frac{1}{3}(3)+5=6$, so $(3,6)$

Step5: Graph second line ($y=-2x-2$)

• y-intercept: $(0,-2)$
• Second point: when $x=-1$, $y=-2(-1)-2=0$, so $(-1,0)$

Answer:

The solution to the system is the intersection point $(-3, 4)$. To graph:

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

The lines intersect at $(-3, 4)$.