Question

solve the following system of equations graphically on the set of axes below.$y = -\frac{1}{4}x - 7$$y = x - 2$plot two lines by clicking the graph.click a line to delete it.

Explanation:

Step1: Find intercepts for $y=-\frac{1}{4}x-7$

• x-intercept: Set $y=0$:

$0 = -\frac{1}{4}x -7 \implies \frac{1}{4}x = -7 \implies x = -28$

• y-intercept: Set $x=0$:

$y = -\frac{1}{4}(0) -7 = -7$
Points: $(-28, 0)$ and $(0, -7)$

Step2: Find intercepts for $y=x-2$

• x-intercept: Set $y=0$:

$0 = x -2 \implies x=2$

• y-intercept: Set $x=0$:

$y = 0 -2 = -2$
Points: $(2, 0)$ and $(0, -2)$

Step3: Solve algebraically to find intersection

Set equations equal:
$-\frac{1}{4}x -7 = x -2$
Multiply all terms by 4 to eliminate fraction:
$-x -28 = 4x -8$
Rearrange terms:
$-28 +8 = 4x +x$
$-20 = 5x \implies x = -4$
Substitute $x=-4$ into $y=x-2$:
$y = -4 -2 = -6$

Answer:

The solution (intersection point of the two lines) is $(-4, -6)$. To graph:

1. For $y=-\frac{1}{4}x-7$, plot $(0, -7)$ and $(-28, 0)$, then draw the line through them.
2. For $y=x-2$, plot $(0, -2)$ and $(2, 0)$, then draw the line through them.
3. The lines intersect at $(-4, -6)$.