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 $y=-\frac{1}{4}x-7$

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

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

For x-intercept: set $y=0$,
$0 = x - 2$
$x = 2$
For y-intercept: set $x=0$,
$y = 0 - 2 = -2$
Points: $(2, 0)$ and $(0, -2)$

Step3: Find intersection algebraically

Set equations equal:
$-\frac{1}{4}x -7 = x -2$
$-7 + 2 = x + \frac{1}{4}x$
$-5 = \frac{5}{4}x$
$x = -5 \times \frac{4}{5} = -4$
Substitute $x=-4$ into $y=x-2$:
$y = -4 -2 = -6$

Answer:

The solution (intersection point) 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.

The lines cross at $(-4, -6)$.