The graph of a linear function is a straight, non-vertical line. To determine whether the relation in the table is a linear function, let's first confirm that the relation is a function.

Words

Since each input $x$ has only one output, the relation in the table is a function. Let's look for a pattern of change in the given table.

Change in $x$	$x$	$y$	Change in $y$
	$0$	$5$
$+ 1$	$1$	$8$	$+ 3$
$+ 1$	$2$	$11$	$+ 3$
$+ 1$	$3$	$14$	$+ 3$

We can see that every time the

x -

values increase by

1,

the

y -

values increase by

3 .

This might lead us to believe that the relationship is just

3

times

x .

However, by testing the values of

x

with this relationship, we can see that the resulting values of

y

are not equal to the given values.

3 \cdot x 3 \cdot 0 3 \cdot 1 = ? y \neq = 5 \neq = 8

Assuming

y

is equal to

3

times

x,

the values of

y

are

5

less than we need in each case. Therefore, we can say that the value of

y

is equal to

3

times

x

plus

5 .

Equation

To describe the relation with an equation, let's translate our verbal description into algebraic terms.

the value of y is equal to 3 times x plus 5 y = 3 x + 5

Graph

Now let's graph the points. By doing so, we will also be able to determine if the relationship is a linear function.

The graph of a linear function is a straight, non-vertical line. Now that we have graphed the given points, we can see that they are able to be connected with a straight line. The relationship is therefore linear.

Exercise

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