find the equation of the linear function represented by the table below in slope-intercept form.

Explanation:

Step1: Calculate the slope (m)

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Let ((x_1,y_1)=(1,-7)) and ((x_2,y_2)=(2,-11)). Then (m=\frac{-11-(-7)}{2 - 1}=\frac{-11 + 7}{1}=-4)

Step2: Use the point - slope form (y - y_1=m(x - x_1))

We know (m=-4) and take the point ((x_1,y_1)=(1,-7)). The point - slope form is (y-(-7)=-4(x - 1))

Step3: Simplify to slope - intercept form (y=mx + b)

Expand (y + 7=-4x+4). Subtract 7 from both sides: (y=-4x+4 - 7), so (y=-4x-3)

Answer:

(y=-4x - 3)