write an equation to represent the table in slope - intercept form.

Explanation:

Step1: Find the slope (m)

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Let's take two points ((x_1,y_1)=(-2,0)) and ((x_2,y_2)=(-1,-6)). (m=\frac{-6 - 0}{-1-(-2)}=\frac{-6}{1}=-6)

Step2: Find the (y -)intercept (b)

The slope - intercept form is (y = mx + b). We can use the point ((x = 0,y=-12)) (since when (x = 0), (y=b) in (y=mx + b)). So (b=-12)

Step3: Write the equation

Substitute (m=-6) and (b = - 12) into (y=mx + b). The equation is (y=-6x-12)

Answer:

(y=-6x - 12)