IXL - Identify linear functions from tables (Algebra 1 practice)

The table shows a function. Is the function linear or nonlinear?

x	y
6	0
7	10
8	20

linear

nonlinear

ref_doc_title.

Learn with an example

question

The table shows a function. Is the function linear or nonlinear?

x	y
17	19
18	12
19	5

linear

nonlinear

key idea

A linear function has a constant rate of change. A nonlinear function does not.

A function's rate of change between two points

(

)

and

(

)

is:

–

A function has a constant rate of change if its rate of change is the same between any two points.

solution

To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.

Pick any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.

Rows 1 and 2:

x	y
17	19
18	12
19	5

Call the values in the first row

and

Call the values in the second row

and

Rate of change

–

Now pick a different pair of rows and calculate the rate of change between them.

Rows 1 and 3:

x	y
17	19
18	12
19	5

Call the values in the first row

and

Call the values in the third row

and

Rate of change

–

The two rates of change are the same.

If you checked the rate of change between rows 2 and 3, you would find that it is also

–

This means the rate of change is the same for each pair of points. So, the function has a constant rate of change.

The function is

linear.

Looking for more? Try these:

Lesson: Linear functions

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	06

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

CC.8Write a linear function from a table

N.1Identify linear functions from graphs and equations

Lesson: Linear functions

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!