Question

A linear function includes the points (2, 3) and (6, 8). What is the rate of change of the linear function?

Write the answer as an improper fraction (fraction greater than one) in lowest terms.

Answer 1

The rate of change of a linear function = 5/4

Explanation:

Given that a linear function includes the points (2, 3) and (6, 8).

So we have the points

• (2, 3)

• (6, 8)

We know that the rate of change of a function is also termed as the slope of the function.

In other words, the slope of the linear function gives us the rate of change of the linear function.

Thus,

Determining the rate of change or slope between (2, 3) and (6, 8)

• (x₁, y₁) = (2, 3)

• (x₂, y₂) = (6, 8)

Using the formula

Rate of change = Slope = [y₂ - y₁] / [x₂ - x₁]

= [8 - 3 / [6 - 2]

= 5 / 4

Thus, the rate of change of a linear function = 5/4