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

Answer:

D) 1/2

Step-by-step 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