Montana Math MT.CORE.ALG.FUN.6

MathGrades 9–12Understand Functions and Expressions

The Standard

Understand that a graph of an equation in two variables is the set of all of its solutions plotted in a coordinate plane.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What Students Need to Do: Students check whether an ordered pair solves an equation by substituting its coordinates. They plot solutions and recognize that the graph includes every point that works, not just the points they first marked.
What Mastery Looks Like: Given x + 2y = 6, a student can plot (0, 3) and (2, 2), then verify that (1, 2.5) also lies on the line. They can show why (3, 2) does not belong.
Common Misconceptions: Some students think only the points they plotted are solutions, so they leave gaps in the line. Others switch x and y when substituting or assume any point on the grid works.
How to Assess It: On graph paper, draw the full graph of x + 2y = 6 using (0, 3) and (6, 0). Check (2, 2) and (3, 2) by substitution, then mark which belongs on the graph.

Lesson moves

Give pairs graph paper and x + 2y = 6; have them plot three solutions, draw the line, and check (1, 2.5).
Ask students to write why (1, 2.5) belongs on the graph of x + 2y = 6, even if they did not plot it first.
Play point detective with cards showing (2, 2), (3, 2), and (1, 2.5); students sort them by whether they solve x + 2y = 6.
Graph x + 2y = 6 for $1 pencils and $2 notebooks, then mark which points represent purchases of whole items.

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