NY Next Generation Math NY-8.F.3

Math8th GradeDefine, evaluate, and compare functions.

The Standard

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students interpret y = mx + b as a linear relationship whose graph is a straight line. They distinguish linear functions from nonlinear functions using equations, tables, and graphs.

What Mastery Looks Like

The student connects m to constant rate and b to the vertical intercept in a straight-line graph. The student identifies a squared or changing-rate relationship as nonlinear.

Common Misconceptions

Students may assume every equation with x and y is linear or that every graph through points is a line. They may confuse a curved graph with a steep straight line.

How to Assess It

Give y = 3x - 2, y = x squared, and two matching graphs. Ask students to classify each function and justify the classifications.

Lesson moves

Ways to Teach It

  1. Plot values from linear and nonlinear equation cards, then compare the shapes and changes between points.

  2. Ask students how constant differences in a table appear in the graph of a linear function.

  3. Play linear-or-nonlinear match using equations, tables, graphs, and verbal descriptions.

  4. Compare a constant hourly charge with an area-growth relationship and classify each model.

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