Identify linear functions from graphs and equations

Distinguish linear functions by constant rate of change and straight-line graphs.

Do this: Read the concept below, then try the quiz or activity.

Lesson 51 of 192
26%

Concept

Objective: Students will identify linear vs non-linear relationships from equations and graphs.

Estimated Time: 12 minutes

Standards:
HSF-IF.B.4HSF-IF.C.7

Linear functions have the form y = mx + b and graph as straight lines with constant slope.

Try it

Decide whether y = 4x - 7 and y = x² + 1 are linear, then justify.

📈 Coordinate Grapher

Switch function types and observe when the graph remains linear.

y = y = 1x
-10-9-8-7-6-5-4-3-2-112345678910-10-9-8-7-6-5-4-3-2-112345678910

Concept Check

Which equation is linear?

Concept Check

A graph with constant slope is:

Common Misconception
Always verify your result in context instead of trusting a first pass.

Linear identification checklist

These steps are out of order — can you fix them?

1.Conclude linear/nonlinear
2.Verify equation is y = mx + b
3.Check if slope is constant
4.Check graph shape

Short Answer

Name one sign that a relation is not linear.

Mastery Check

Pass this check with at least 80% to unlock completion.

Question 1

Which equation is linear?

Question 2

A graph with constant slope is:

Pass the mastery check (80%+) to unlock completion.