Question

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

Explanation:

Step1: Find intercepts for $y=-x-2$

• y-intercept: Set $x=0$, $y=0-2=-2$, so point $(0,-2)$.
• x-intercept: Set $y=0$, $0=-x-2 \implies x=-2$, so point $(-2,0)$.

Step2: Find intercepts for $y=2x-8$

• y-intercept: Set $x=0$, $y=0-8=-8$, so point $(0,-8)$.
• x-intercept: Set $y=0$, $0=2x-8 \implies x=4$, so point $(4,0)$.

Step3: Solve for intersection algebraically

Set $-x-2=2x-8$
$\implies -x-2x=-8+2$
$\implies -3x=-6$
$\implies x=2$
Substitute $x=2$ into $y=-x-2$: $y=-2-2=-4$
Intersection point: $(2,-4)$

Answer:

1. For $y=-x-2$: Plot points $(-2,0)$ and $(0,-2)$, then draw the line through them.
2. For $y=2x-8$: Plot points $(4,0)$ and $(0,-8)$, then draw the line through them.
3. The solution to the system is the intersection point $(2, -4)$.