Montana Math MT.CORE.ALG.LIN.4.c
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 slope-intercept form, the rate of change, and the initial value,
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students read an equation in the form y = mx + b. They identify m as the change in y for each increase of 1 in x, and b as the value of y when x is zero.
What Mastery Looks Like
- Given y = -2x + 10, a student says the value starts at 10 and drops by 2 each time x increases by 1. They can find (0, 10) on a graph and show the same pattern in a table.
Common Misconceptions
- Students may call b the slope because it is the number added. They may call the first value in a table the initial value, even when its x-value is not zero.
How to Assess It
- Exit ticket: A scooter rental costs $6 to start and $3 per hour. Write an equation for the cost y after x hours, then name the rate of change and initial value with units.
Lesson moves
Ways to Teach It
Give pairs four blue counters for a starting fee and two red counters per mile; build costs for zero to three miles, then write y = 2x + 4.
Write two sentences explaining why y = 3x + 8 describes an $8 signup fee plus $3 per visit, including the cost at zero visits.
Have pairs match y = 2x + 4 and y = 4x + 2 to tables with rows (0, 4), (1, 6) and (0, 2), (1, 6).
Post a parking sign reading '$5 to enter, $2 per hour'; students write y = 2x + 5 and find the cost for three hours.
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Related Standards
- MT.CORE.ALG.LIN.4.d
Understanding the relationship between point-slope form, the rate of change, and a given point, and
- 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.3.a
Identifying the rate of change and initial value in each representation.
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