Question

What is the rate of change and initial value for the linear relation that includes the points shown in the table?

xy
110
28
36
44
Initial value: 12, rate of change: −2
Initial value: 8, rate of change: 2
Initial value: 12, rate of change: 2
Initial value 8, rate of change: −2

Answer 1

Remember that

In a linear equation

y=mx+b

the rate of change is the same that the slope m

and the initial value is b

so

step 1

Find out the slope

we take the points (2,3) and (4,5)

m=(5-3)/(4-2)

m=2/2

m=1

step 2

Find out the equation of the line

y=mx+b

we have

m=1

point (2,3)

substitute and solve for b

3=(1)(2)+b

3=2+b

b=1

therefore

The rate of change is 2 and the initial value is 1