Montana Math MT.CORE.ALG.LIN.4

MT.CORE.ALG.LIN.4 is a cluster heading. These are the individual standards under it.

• MT.CORE.ALG.LIN.4.a

  Choosing the form strategically when writing an equation based on given information and intended use,

• 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,

• 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.4.e

  Understanding the relationship between standard form and the x- and y-intercepts.

01

What Students Need to Do

Students choose an equation form that fits the information they have or the question they need to answer. They rewrite lines in different forms and use each one to find a rate of change, starting value, given point, or intercepts.

02

What Mastery Looks Like

Given slope 2 and point (1, 4), a student writes y - 4 = 2(x - 1), y = 2x + 2, and 2x - y = -2. They use these forms to identify the starting value, 2, and the intercepts, (-1, 0) and (0, 2).

03

Common Misconceptions

Students may treat the constant in y = mx + b as the x-intercept, or mistake a given point's y-value for the starting value. They may drop signs when expanding point-slope form or mistake the coefficients in standard form for the intercepts.

04

How to Assess It

Exit ticket: A line passes through (4, 1) with slope -1/2. Write its equation in all three forms, then find both intercepts.

1. 01

   On graph paper, plot (2, 3), use a slope triangle with rise 1 and run 2, then write three equations for the line.

2. 02

   Ask: If you know a line's slope and one point, which equation form would you write first, and why?

3. 03

   Hand out cards showing equations in three forms; partners match equivalent equations and check each match by finding the slope and intercepts.

4. 04

   Give students a $24 budget for $4 student tickets and $6 adult tickets; have them graph 4x + 6y = 24 and explain both intercepts.

• MT.CORE.ALG.QUAD.3

  Understand that quadratic expressions can be represented in multiple forms and the specific features of each form by: Choosing the form strategically when writi...