Question

What is the rate of change and initial value for the linear relation that includes the points shown in the table? x; 1,3,5,7

y; 20,10,0,-10

Answer 1

The rate of change is -5

The initial value is 25

Explanation:

Since, this is a linear relation

so, we can select any two points and find equation of line

points are (1,20) and (3,10)

so,

`x_1=1,y_1=20`

`x_2=3,y_2=10`

now, we can find slope

`m=(y_2-y_1)/(x_2-x_1)`

now, we can plug values

`m=(10-20)/(3-1)`

`m=-5`

now, we can use point slope form of line

`y-y_1=m(x-x_1)`

now, we can plug values

`y-20=-5(x-1)`

now, we can solve for y

`y=-5x+25`

we know that

slope is the rate of change

So, the rate of change is -5

For finding initial value , we can plug x=0 and find y

`y=-5* 0+25`

`y=25`

So, initial value is 25