Question

write an equation of the line.
the image shows a coordinate grid with a line passing through (-2, 2) and having a slope m = -2.

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
We know that $m=-2$ and the point $(x_1,y_1)=(-2,2)$.

Step2: Substitute values into point - slope form

Substitute $m = - 2$, $x_1=-2$ and $y_1 = 2$ into the point - slope formula:
$y - 2=-2(x-(-2))$
Simplify the right - hand side: $y - 2=-2(x + 2)$

Step3: Expand and simplify to slope - intercept form (optional, but to get a more standard form)

Expand the right - hand side: $y-2=-2x-4$
Add 2 to both sides of the equation: $y=-2x-4 + 2$
Simplify the constants: $y=-2x-2$

Answer:

The equation of the line is $y=-2x - 2$ (or in point - slope form $y - 2=-2(x + 2)$)