Question

Given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

Answer 1

To determine wether of not it is linear, you will need to see if it has a constant rate of change, if it does it is a linear function, if it doesn't it is non-linear. and to find the rate of change you will need to find the slope.

Answer 2

A linear function is represented using a straight line.

• The rate of change is calculated using $m = \frac{y_2 -y_1}{x_2 -x_1}$.
• If the graph has a uniform slope, it is linear. Otherwise, it is not.

To calculate the rate of change of a function, pick any two points on the graph and apply the following formula for rate of change

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

Take for instance:

$(x_1,y_1) = (1,5)$

$(x_2,y_2) = (2,7)$

The rate of change (m) is:

$m = \frac{7-5}{2 -1}$

$m = \frac{2}{1}$

$m = 2$

So, the rate of change is 2

To check if the function is linear or not.

Pick another point on the graph, then calculate the slope using the same formula.

Let another point be:

$(x_3,y_3) = (3,9)$

The rate of change using the following points:

$(x_3,y_3) = (3,9)$ and $(x_1,y_1) = (1,5)$

is as follows:

$m = \frac{9 - 5}{3 - 1}$

$m = \frac{4}{2}$

$m =2$

Since the rate of change is unchanged (i.e. 2) in both computations, then the function is linear.

If the value changes, then the function is nonlinear.

Read more about linear and nonlinear functions at:

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