Montana Math MT.CORE.ALG.LIN.3.c

MathGrades 9–12Linear Functions and Expressions

The Standard

MT.CORE.ALG.LIN.3: Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: Identifying the rate of change and initial value in each representation. Converting between representations, and Writing equations for a line perpendicular or parallel to a given line that passes through a given point.

Represent linear functions using tables, graphs, equations, and verbal situations, while using technology strategically. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: Writing equations for a line perpendicular or parallel to a given line that passes through a given point.

2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning

Teacher's field guide

What This Standard Means

What Students Need to Do: Students model a straight route with words, a table, a graph, and an equation. They write parallel and perpendicular equations through a given point. They use a graphing tool to check their work.
What Mastery Looks Like: Students can write both equations through a given point and make tables and graphs that match. They know parallel lines have the same slope and perpendicular slopes are negative reciprocals. They also recognize that horizontal and vertical lines are perpendicular.
Common Misconceptions: Students may change the slope for a parallel line or only change its sign for a perpendicular line. Some use the original line's intercept instead of finding a new one through the given point. Others forget that horizontal and vertical lines are perpendicular.
How to Assess It: Exit ticket: Given y = 2x + 1 and (3, 4), write the parallel and perpendicular equations through the point. For one new line, give two table rows and describe its graph in words.

Lesson moves

Ways to Teach It

Use yarn on graph paper to model y = 2x + 1; pin (3, 4), then place yarn lines parallel and perpendicular through the pin.
Write directions for a route through (3, 4) parallel to y = 2x + 1; explain why your equation and table fit.
In Desmos, plot y = 2x + 1 and (3, 4); race to graph a parallel and a perpendicular line through the point.
Use a map near Salish Kootenai College, a tribal college in Pablo, to model a perpendicular to a straight road through a chosen point.

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