Linear Functions and Applications

Lesson 3

Math

Unit 1

11th Grade

Lesson 3 of 13

Objective


Solve for a desired quantity in a linear function.

Common Core Standards


Core Standards

  • A.CED.A.1 — Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
  • A.CED.A.4 — Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R.

Foundational Standards

  • 8.F.B.4

Criteria for Success


  1. Identify missing values in a linear function presented algebraically. 
  2. Given an equation and context, solve for a quantity algebraically.
  3. Describe what the function models once solved for a variable.

Tips for Teachers


This lesson teaches skills similar to what students learned in Algebra 1; however, because of the relationship to inverse functions, use this skill as a way to review concepts and understand the topic conceptually before applying notation and the definition of inverse functions more formally in the next lesson.

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Anchor Problems

25-30 minutes


Problem 1

The equation below is the equation of a line in the $${ xy- }$$ plane, and $$t$$ is a constant. 
If the slope of the line is $${-2}$$, what is the value of $$t$$?

$$tx + 8y = -4 $$

Guiding Questions

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Problem 2

Alex is working on a budget after getting a new job. 

  • She has budgeted herself $170/month on eating out for dinner. 
  • Every month she has a standing dinner date with a friend, for which she pays $20 (because they always go to the same place and she gets the same thing to eat). 
  • A quarter of the times she goes out to eat, she will spend half of the usual amount she spends MORE because she knows she will want to go out to fancier places every once in a while. 

There are two ways to Alex can think about modeling this situation: 

  • The amount of times, $$x$$, she can go to eat as a function of how much each meal costs, $$c$$
  • The amount each meal costs, $$c$$, as a function of how many times she goes out to eat, $$x$$

Below is the equation that shows the total amount she has budgeted herself based on the amount each meal costs and the amount of times she goes out. 

$$(c \cdot x)+ (\frac{1}{2}c)(\frac{1}{4}x)+20=170$$

  1. Annotate this problem with what each part means. 
  2. Write an equation for each of the following models: 
  1. The amount of times, $$x$$, she can go to eat as a function of how much each meal costs, $$c$$
  2. The amount each meal costs, $$c$$, as a function of how many times she goes out to eat, $$x$$

Guiding Questions

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Target Task

5-10 minutes


Anton writes a model that describes the number of tacos his friends eat as a function of the cost of the total tacos. Below is a graph of the model. 

Anton writes a second model that describes the total cost of the tacos as a function of the number of tacos his friends eat. Below is a graph of the model. 

  1. Label the axes appropriately. Which one makes more sense? 
  2. How are these two graphs similar? Different? 
  3. How are these two equations similar? Different? 

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems that mimic the thinking required in Anchor Problem #2. 

Next

Find the inverse of a contextual situation graphically and describe the meaning of the function and its inverse.

Lesson 4
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Linear Functions

Topic B: Systems of Functions and Constraints

Topic C: Piecewise Functions

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