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

Answer:

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  

$m=\frac{y2-y1}{x2-x1}$  

we have

$A(1,10)\ B(2,8)$  

Substitute the values  

$m=\frac{8-10}{2-1}$

$m=-2$  ----> 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