Montana Math MT.CORE.ALG.LIN.4.a
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: Choosing the form strategically when writing an equation based on given information and intended use,
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students choose an equation form that fits the information they have, such as a slope and point or a slope and y-intercept. They write the equation and explain why they chose that form.
What Mastery Looks Like
- Given slope -2 and point (3, 5), a student writes y - 5 = -2(x - 3) without finding the y-intercept first. Given a slope and y-intercept, they write a slope-intercept equation directly.
Common Misconceptions
- Students often treat the y-value of any given point as the y-intercept. In point-slope form, they may write x + 3 instead of x - 3 for a point with x-coordinate 3.
How to Assess It
- Exit ticket: A line has slope -2 and passes through (3, 5). Write its equation in the form that takes the fewest steps, and explain your choice.
Lesson moves
Ways to Teach It
On graph paper, plot (3, 5), draw a line with slope -2, then write point-slope and slope-intercept equations for it.
Ask, “You know a line passes through (3, 5) with slope -2. Which form takes fewer steps, and why?”
Match slope-and-point cards and slope-and-intercept cards to equation forms, then write each equation and check it by substitution.
Give a taxi receipt for $17 at 4 miles and a $3-per-mile rate; ask students to write a fare equation from those facts.
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