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

Answer 1

Answer:

The rate of change is -5

The initial value is 25

Step-by-step 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

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{10-20}{3-1}$

$m=-5$

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

$y=-5\times 0+25$

$y=25$

So, initial value is 25