Question

What is the rate of change for the function? and what is the initial value of the function?

Answer 1

Find the slope-intercept formula:

y= mx+b

Where:

m = slope (rate of change)

b= y-intercept ( initial value)

Apply the slope formula:

`m=\text{ }(y2-y1)/(x2-x1)`

where the coordinates points are from the table:

(x1,y1) = (-5,7)

(x2,y2) = (-3,1)

Replace:

`m=\text{ }(1-7)/(-3-(-5))=(-6)/(2)=-3`

So far we have:

y= -3x+b

Replace (x,y) by a coordinate point from the table (-5,7)and solve for b

7 = -3(-5) + b

7= 15+b

7-15 = b

-8 = b

Equation:

y= -3x-8

rate of change: -3

initial value = -8