Question

1. $y=-2x+2$

$y=-2x-2$

Explanation:

Step1: Identify slope-intercept form

Both equations use $y=mx+b$, where $m$=slope, $b$=y-intercept.
For $y=-2x+2$: $m=-2$, $b=2$
For $y=-2x-2$: $m=-2$, $b=-2$

Step2: Plot y-intercepts

For $y=-2x+2$: mark $(0, 2)$
For $y=-2x-2$: mark $(0, -2)$

Step3: Use slope to find 2nd points

Slope $m=-2=\frac{-2}{1}$. From $(0,2)$: move 1 right, 2 down to $(1, 0)$. From $(0,-2)$: move 1 right, 2 down to $(1, -4)$.

Step4: Analyze the system

Same slope ($m=-2$), different y-intercepts mean parallel lines, no intersection.

Answer:

The two lines are parallel and never intersect, so the system has no solution.
(Graph details: $y=-2x+2$ passes through $(0,2)$ and $(1,0)$; $y=-2x-2$ passes through $(0,-2)$ and $(1,-4)$)