Question

11)

linear function
ху
94
30
-3
-4
-9-8
The values in the table represent a linear function. How does the value of y change in relation to a change in the
value of x?
A)
for every change in x by -6, y changes by 4
B)
for every change in x by 6, y changes by -4
for every change in x by -4, y changes by-6
D)
for every change in x by-6, y changes by -4

Answer 1

For every change in x by -6, there is a corresponding change in y by -4

Explanation:

Given

x ---- y

9 --- 4

3 --- 0

-3 -- -4

-9 -- -8

Required

Determine the rate of change

To do this, we simply get an expression for the slope.

Take any two corresponding x and y values.

`(x_1,y_1)= (9,4)`

`(x_2,y_2)= (3,0)`

The slope (m) is:

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

This gives:

`m = (0 - 4)/(3 - 9)`

`m = (- 4)/(-6)`

This can then be represented as:

`(y_2 - y_1)/(x_2 - x_1) = (- 4)/(-6)`

It means that:

For every change in x by -6, there is a corresponding change in y by -4