Question

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

x y
1 10
2 8
3 6
4 4
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

Initial value
`12`, rate of change:
`-2`

Step-by-step explanation:

Step 1

Find the rate of change

we know that

In a linear equation the rate of change is equal to the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

`A(1,10)\ B(2,8)`

Substitute the values

`m=(8-10)/(2-1)`

`m=-2` ----> rate of change

Step 2

Find the initial value

The equation of the line into slope-point form is equal to

`y-y1=m(x-x1)`

Substitute

`y-10=-2(x-1)`

`y=-2x+2+10`
`y=-2x+12`

The initial value is the value of y when the value of x is equal to zero (is the y-intercept)

`y=-2*0+12=12`----> initial value