Question

What is the rate of change of a linear function that includes the points (5, 2) and (9, 4)?

A) -2
B) 2
C) 4
D) 1/2
1
2

Answer 1

D) 1/2

Explanation:

A linear function has the following format:

`y = ax + b`

In which a is the slope, that is, the rate of change of the function and b is the y-intercept, that is, the value of y when x = 0.

We have that:

Point (5,2), which means that when x = 5, y = 2. So

`y = ax + b`

`5a + b = 2`

Point (9,4), which means that when x = 9, y = 4. So

`9a + b = 4`

I am going to write b as a function of a in the second equation, and replace on the first. So

`b = 4 - 9a`

Then

`5a + b = 2`

`5a + 4 - 9a = 2`

`-4a = -2`

`4a = 2`

`a = 1/2`

This means that the slope, which is the rate of change of the function, is 1/2.

So the correct answer is:

D) 1/2