Chapter 4A: Linear Functions
Chapter 4A: Linear Functions
Index:
1: Proportional Relationships ? U4L1
Pg. 2
2: Conversions ? U4L2
Pg. 11
3: Non-proportional Linear Relationships ? U4L3
Pg. 17
4: Graphing Linear Equations Introduction
Pg. 24
5: More Work Graphing Linear Functions ? U4L4
Pg. 31
F: Graphing Linear Equations (Day 2)
Pg. 37
6: Writing Equations in Slope-Intercept Form ? U4L5
Pg. 45
7: Modeling with Linear Functions ? U4L6
Pg. 52
8: More Linear Modeling ? U4L7
Pg. 57
9: Strange Lines ? Horizontal and Vertical ? U4L8
Pg. 63
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10: Absolute Value and Step Functions ? U4L9 11: The Truth About Graphs ? U4L10 12: Graphs of Linear Inequalities ? U4L11 13: Introduction to Sequences ? U4L12 14: Arithmetic Sequences ? U4L13
Pg. 68 Pg. 73 Pg. 78 Pg. 83 Pg. 88
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Name:_____________________________________________________ Algebra I
Lesson 1:
Date:_________________ Period:_________ Proportional Relationships
Proportional Relationships
You have studied proportional relationships in previous courses, but they are the basis of all linear functions, so we will take a lesson to recall their particulars Two variables have a proportional relationship if their respective values are always in the same ratio (They have the same relative size to one another).
For Example: A rope's length and weight are in proportion. When 20meters of rope weights 1kilogram, then:
- Now using the given information lets establish a ratio:
- You can now use this ratio in a proportion, which can help you solve for missing information. - How much would 40 meters of rope weight?
o
Cross Multiply Isolate the variable Therefore 40 meters of that rope will weight 2 kilograms
3
Exercise #1: At a local farm stand, six apples can be bought for four dollars. Determine how much it would
cost to buy the following amounts of apples. Round to the nearest cent, as necessary.
(a) Identify the given ratio
(b) 12 apples
(c) 20 apples
(d) If c is the total cost of apples and n is the number of apples bought, write a proportional relationship between c and n. Solve this equation for the variable c.
(e) Use the equation from part d and graph the relationship on the grid below.
(f) According to the graph,
. Illustrate this on your graph. How do you interpret
in
terms of apples and money spent?
4
Exercise #2: Erika is driving at a constant rate. She travels 120 miles in the span of 2 hours.
(a) If Erika travels at the same rate, how far
(b) Write a proportional relationship between the distance D
will she travel?
that Erika will drive over the time t that she travels,
assuming she continues at this same rate. Solve the
proportion for D as a function of t.
(c) What is the value of the proportionality constant? What are its units?
(d) How much time will it take for Erika to travel 150 miles?
(e) Graph D as a function of t on the axes to the right.
(f) What does the constant of proportionality from part (c) represent about this graph. Explain your thinking. 5
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