Before we begin, let's take a look at the information given in the table of values.

$x$	$0$	$1$	$2$	$3$	$4$
$y$	$12$	$13$	$14$	$15$	$16$

The graph of a linear function is a single, straight line in a coordinate plane. To know if the data given in the table represents a linear function, let's first plot the points as $(x, y)$ coordinate pairs.

Connecting these points will form a straight line if the function is linear. Otherwise, we will have shown that the function is nonlinear.

Since we can use a straight edge to connect all of the given points, we know that they lie on the same line in the coordinate plane. This means that the function is linear.

Extra

Using the Rate of Change

We can also know if a function is linear by looking at the rate of change. A constant rate of change means that a function is linear. Rate of change tells us how many units a function moves up or down in comparison to how many units the function moves to the right. We usually call this the change in

y

over change in

x

or, more casually, the rise over run.

\frac{change in y}{change in x} = \frac{rise}{run}

Let's look at the given table to find the rate of change for this function.

Each time the value of

x

increases by

1,

the value of

y

also increases by

1 .

This means that the rate of change is

1 .

\frac{change in y}{change in x} = \frac{1}{1} = 1

Because the rate of change is constantly

1

for every change in

x,

we know that our function is linear!

Exercise

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