write the equation of this line in slope-intercept form.

Explanation:

Step1: Identify two points

From the graph, we can see two points on the line: let's take ((-4, 8)) and ((0, -8)) (the y - intercept).

Step2: Calculate the slope (m)

The formula for slope (m=\frac{y_2 - y_1}{x_2 - x_1}). Using the points ((x_1,y_1)=(-4,8)) and ((x_2,y_2)=(0, - 8)), we have (m=\frac{-8 - 8}{0-(-4)}=\frac{-16}{4}=-4).

Step3: Determine the y - intercept (b)

The y - intercept (b) is the value of (y) when (x = 0). From the point ((0,-8)), we know that (b=-8).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is (y=mx + b). Substituting (m=-4) and (b = - 8) into the formula, we get (y=-4x-8).

Answer: (y = - 4x-8)