Montana Math MT.CORE.ALG.LIN.4.d
The Standard
- MT.CORE.ALG.LIN.4
- Understand that linear equations can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writing an equation based on given information and intended use, Converting between slope-intercept, point-slope, and standard form symbolically, Understanding the relationship between slope-intercept form, the rate of change, and the initial value, Understanding the relationship between point-slope form, the rate of change, and a given point, and Understanding the relationship between standard form and the x- and y-intercepts.
Understand that linear equations can be represented in multiple forms and the specific features of each form by: Understanding the relationship between point-slope form, the rate of change, and a given point, and
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write a line's equation from its rate of change and one point. They identify the slope and point in point-slope form, then connect the equation to its graph.
What Mastery Looks Like
- Students can write y-5=3(x-2) for a line with slope 3 through (2,5) and explain each number. They can use another point on the line to write an equivalent equation.
Common Misconceptions
- Some students write (x+2) instead of (x-2) for a point at (2,5). Others treat 5 as the y-intercept, even though the point's x-coordinate is not zero.
How to Assess It
- Exit ticket: Write a point-slope equation for a line with slope 3 through (2,5). Substitute the point to check your equation.
Lesson moves
Ways to Teach It
On a coordinate pegboard, students stretch a rubber band through (1,2) and (3,6), then count rise and run and write the equation.
Ask students to compare y-2=2(x-1) and y-6=2(x-3), then explain whether they draw the same line.
Give pairs cards with slopes, points, equations, and graphs; students match sets and explain how they know each match works.
A taxi fare is $8 at 2 miles and rises $3 per mile; students write a point-slope equation for the fare.
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Related Standards
- MT.CORE.ALG.LIN.2
Understand slope as a rate of change and y-intercept as the initial value.
- MT.CORE.ALG.LIN.4
Understand that linear equations can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writing an...
- MT.CORE.ALG.LIN.4.b
Converting between slope-intercept, point-slope, and standard form symbolically,
- MT.CORE.ALG.LIN.4.c
Understanding the relationship between slope-intercept form, the rate of change, and the initial value,
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