Montana Math MT.8.F.3

Math8th GradeFunctions

The Standard

Interpret the equation y = mx + b as defining a linear function whose graph is a straight line with slope m passing through the point (0, b).

2026 Montana Mathematics Content Standards

Teacher's field guide

What Students Need to Do: Students read m as the change in y for each increase of 1 in x. They locate (0, b) and use the slope to draw the line.
What Mastery Looks Like: Given y = -2x + 3, a student marks (0, 3) and (1, 1), then draws the line. They explain that the line falls 2 units for every 1 unit right.
Common Misconceptions: Students may swap m and b or plot b at (b, 0) instead of (0, b). For a negative slope, they may move down and left instead of down and right.
How to Assess It: Exit ticket: Graph y = -x/2 + 3. Circle where the line crosses the y-axis and label how much y changes when x increases by 2.

Lesson moves

For y = -x/2 + 2, place counters at (0, 2), (2, 1), and (4, 0) on graph paper, then draw the line.
Ask students to compare y = 2x + 1 and y = 2x - 3 in writing, naming what stays the same and what changes.
Give pairs cards with equations, graphs, and slope and intercept labels; have them match each set and explain their choices.
Graph a bike rental that costs $5 to start and $3 per hour, then label (0, 5) and the $3 hourly increase.

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