Montana Math MT.CORE.ALG.LIN.4.e
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 standard form and the x- and y-intercepts.
2026 Montana Mathematics Content Standards · Algebraic and Functional Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find where a line crosses each axis from an equation in standard form. They set the other variable to zero, then use the two points to graph the line.
What Mastery Looks Like
- Given 3x+2y=12, a student finds (4,0) and (0,6). They label each intercept and check both points in the equation.
Common Misconceptions
- Students may switch the x- and y-intercepts or set the wrong variable to zero. Some mistake the coefficients for intercepts and say 3x+2y=12 crosses at 3 and 2.
How to Assess It
- Exit ticket: For 4x+3y=12, find and label both intercepts. Show which variable you set to zero for each.
Lesson moves
Ways to Teach It
On graph paper, plot the intercepts of 2x+3y=12 in two colors, then draw the line through them.
Ask students to write why setting y to zero finds the x-intercept of 3x+2y=12.
Match cards showing 2x+3y=12, its graph, and its intercepts, (6,0) and (0,4).
Use a $12 budget for $3 notebooks and $2 pens; find what each intercept means when buying only one item.
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Related Standards
- MT.CORE.ALG.QUAD.3.d
Understanding the relationship between vertex form and the vertex of the function.
- MT.CORE.ALG.QUAD.3.c
Understanding the relationship between factored form and the zeros of the function, and
- 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,
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