Alg1 Lesson 1.10: Linear Functions

Lesson 1.10: Linear Functions

Obj: 2A, 2B, 2C, 3B, 3C, 6A, 9A, 12A, 12B: I can
write, graph, and evaluate linear functions.

EQ: How do I evaluate a linear function? (12B)

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas, vocab,

and prior knowledge

● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

What role are you doing today?

• Scribe

• Facilitator

• Includer

• Resourcer

● Go to your calendar paper.

● Select a skill to work on.

● Work on Deltamath.

When waiting for other groups to be ready…

Part 1: Inputs & Outputs

Sam’s Road Trip-Scenario

Formula: M = 58h + 135

What quantities were involved?

What do we know, the hours
traveled or the mile marker
passed?

What we know is the input and
what we want to know is the output.

Categorize

Options (10)

hours traveled

what we know

x values

independent variable

domain

mile marker passed

what we want to know

y values

dependent variable

range

Sort each.

Input

Output

Part 2: Defining a Function

Use the Formula M = 58h + 135 to determine the mile marker that
Sam passed at hour 2.

Input

Process

Output

Context

h = 2

M = 58(2) + 135 = 116 + 135 = 251

251

Sam passed mile marker 251 after 2
hours.

Is it possible that Sam could have been at two different mile markers at the same time? Explain

What would it mean for Sam’s road trip if the points (2,251) and (2,255) were both on the graph that gives the relationship between M and h?

Drag and Drop

Is it ​

Placeholder

that Sam could have been at two different mile markers at the same time. If the points (2,251) and (2,255) were both on the graph that gives the relationship between M and h for Sam's road trip, Sam would be ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

not possible

possible

at two places at one time

in between mile markers 251 and 255

Part 3: Function Notation

Function Notation

The equation, M = 58h + 135 is
rewritten as M(h) = 58h + 135 in
function notation.

Function Examples

f(x) = 7x + 1

y = 7x + 1

Function Non-Examples

x² + y² = 1

y² = x + 9

A special relation
with 1 unique output
for each input.

Using the Formula M(h) = 58h + 135, evaluate for various inputs

Input

Process

Output

Context

2

M(2) = 58(2) + 135 = 116 + 135 = 251

251

Sam passed mile marker 251 after 2
hours.

3

7

Multiple Choice

Evaluate M(12)

M(h) = 58h + 135

• 954

• 831

• 696

• 1,678

• 205

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.

Part 4: Graphing a Function

1.10A: Convenience Store

Your friends know that you stop at the local convenience store every morning on your
way to school and get a bottle of juice. For your birthday, they get you a $50 gift card.
Suppose that a small bottle of juice costs $2 and all you ever buy at the store is juice.
(a) Write a function, f, that can be used to track your gift card balance in terms of the number of
bottles of juice, x, you have purchased.
(b) What is the rate of change of this function? What does this mean for this scenario?
(c) What will the graph of the function look like? How do you know?
(d) What does “f (2) = 46” mean in the context of the problem?
(e) Using the format given below, complete the table representing your function by choosing
several different values representing the number of bottles of juice you have purchased and
computing the remaining balance on your gift card. Then, use your table to construct ordered pairs of the form (x, f (x)).
(f) Plot the ordered pairs found in part e on the coordinate grid.

Handout 1.10A: Convenience Store

All of the ordered pairs of numbers (x, f(x)) in the table of values are
input–output pairs for the function. The pairs of numbers also solve the equation y = 50 − 2x. These (x, y) pairs can be plotted on a coordinate plane, resulting in a graph of the function. Plot the points.

Would it be appropriate to draw a line through these points? Explain.

Draw

Draw a picture of juice.

Part 5: Summary & Practice

Functions and Linear Functions

A function is a special relation between two quantities
where each independent variable maps to only one
dependent variable.

A linear function is a relationship between two quantities
with a constant rate of change.

Handout 1.10B: Practice with Linear Functions

For questions 1 and 2:

● Evaluate the function at the specified inputs for x.

Write the input–output pairs in function notation and in a table of values.

● Graph each line by plotting the points you

generated from the function.

For questions 7–10, write an algebraic function rule that can be used to model
each scenario. Then explain what the slope and the vertical intercept mean in the context of the problem.

7. At a local pumpkin patch you can pick your own pumpkins. There is a $5 charge to enter
the patch and then a $0.25 charge per pound of pumpkin. Let p represent the weight of the pumpkin you choose and C( p) represent the total cost of the pumpkin in terms of the weight of the pumpkin.

8. You are skiing down a 1,350 meter ski slope at 60 meters per second. Let t represent your skiing time in seconds and d(t) represent the distance from the bottom of the ski slope.

9. The basement of a building is 40 feet below ground level. The building’s elevator rises at a rate of 5 feet per second. You enter the elevator in the basement. Let t represent the number of seconds you are in the elevator and h(t ) represent how high the elevator has risen (in feet) in t seconds.

10. There is a stack of old algebra books in the library. Each book is 1.25 inches thick. Let b represent the number of books in a stack and s(b) represent the total height of the stack in inches.

Open Ended

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