CCSS.Math.Content.8.F.A.3
The standard
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
Common Core State Standards for Mathematics · Functions
What this standard means
Students need to recognize that equations in the form y = mx + b make straight-line graphs. They should connect m to the rate of change and b to the starting value, then use tables, graphs, and equations to decide whether a function is linear.
Mastery looks like sorting functions from equations, tables, graphs, and situations, and explaining the choice with equal rates of change or a straight line. Students often get stuck thinking any equation with x and y is linear, or they miss nonconstant change in tables like 1, 4, 9.
Ways to teach it
- Have students graph y = 2x + 1, y = x², and y = 3 on grid paper, then sort the graphs as linear or not linear.
- Ask students to write how they can tell from a table whether a function will make a straight line.
- Give a three-row table for each function and ask students to mark linear or not, then justify with rate of change.
- Compare a taxi base fee plus per-mile charge with the area of a growing square, and have students explain which situation is linear.
Plan a lesson for CCSS.Math.Content.8.F.A.3
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