Download The Cartesian Coordinate System - Little Chute Area School District

Algebra
Notes: Linear Functions
The Cartesian Coordinate System
CCS Practice
Plot and label these points on the CCS below.
A (2, 6)
B (-3, 8)
C (4, -6)
D (-5, -8)
E (0, 9)
F (4, 0)
More Practice With the CCS
Determine the coordinates of each of the points plotted below.
C
A
B
F
D
E
Linear Function Notes
Page #1
Algebra
Notes: Linear Functions
Relationships
You are the owner of Lightning Fast Taxi Company which provides service to the greater Fox
Valley area. In order to use your service, customers pay a fee of $2.75 plus an additional $.35
for each minute of riding time.
A Mathematical Perspective
A function is …
Quantity 1:
Quantity 2:
Inputs and Outputs
In a function, one of the quantities is designated as the __________, while the other quantity is
designated as the ____________.
We make this designation as follows:
Our Example
You are the owner of Lightning Fast Taxi Company which provides service to the greater Fox
Valley area. In order to use your service, customers pay a fee of $2.75 plus an additional $.35
for each minute of riding time.
______________________ depends on _______________________
Four Ways of Describing a Function
1.
2.
3.
4.
Linear Function Notes
Page #2
Algebra
Notes: Linear Functions
Expressing a Function Verbally
Write the verbal model for our example below.
Expressing a Function Algebraically
Write the steps for translating a verbal model to an equation in the space below.
Expressing a Function Numerically
C = .35M + 2.75
M
C
When making a table for a function, the _________________ variable always goes on the left,
and the ____________________ variable always goes on the right.
Expressing a Function Graphically
Linear Function Notes
Page #3
Algebra
Notes: Linear Functions
Graphing a Linear Function I
Make a graph of the equation y = -3x + 4.
x
y
Equations With Fractions
Make a graph of the equation y 
x
2
x  3.
3
y
Writing an Equation in Function Form
Solve the following equation for y:
x
3y – 6x = 18
y
Linear Function Notes
Page #4
Algebra
Notes: Linear Functions
Linear Functions: Algebraically
Slope/Intercept form is…
Linear Functions: Numerically
x
y
Linear Functions: Graphically
Algebraic to Graphical
Graph the following linear equations without making a table of values.
y
3
x5
4
y  4x 1
2
y  x2
5
Linear Function Notes
Page #5
y
3
x
2
Algebra
Notes: Linear Functions
Graphical to Algebraic
Write the equations of the lines graphed below.
Numerical to Algebraic
Determine an equation for each of the tables given below.
x
-4
-2
0
2
4
y
-7
-2
3
8
13
x
-2
-1
0
1
2
Horizontal and Vertical Lines
What are the equations of each of these lines?
Linear Function Notes
Page #6
y
-3
1
5
9
13
Algebra
Notes: Linear Functions
A New Problem
Find the equation that was used to make the following table.
x
-7
-4
-1
2
5
y
9
5
1
-3
-7
Find the Equation of This Line
Find the equation of a line through the points (-2, -3) having a slope = 2.
You Try One
What is the equation of the line with a slope of 3/4 containing the point (3, 5)?
Finding the Slope Between Just Two Points
Find the slope of the line between (-7,5) and (4,-12)
Linear Function Notes
Page #7
Algebra
Notes: Linear Functions
New Concept
Find the equation of the line through the points (1,6) and (3, -4)
“What kind of information do I need to write an equation of a line?”
A Graphical Approach
Find the equation of the line through the points (1,6) and (3, -4)
Why is the graphical approach limited?
An Algebraic Approach
Find the equation of the line through the points (1,6) and (3, -4)
Linear Function Notes
Page #8
Algebra
Notes: Linear Functions
Scatter Plots
When an individual learns a new skill, they usually perform the skill more proficiently as time
goes on. An example of such a skill is keyboarding. Most beginning keyboarders do not type as
many words per minute as experienced keyboarders. The following table gives the keyboarding
speed in words per minute for twelve different individuals in comparison to the number of weeks
of keyboarding experience that each individual has.
Experience
(weeks)
Speed
(words per
minute)
4
7
8
1
6
3
5
2
9
6
7
10
33
45
49
20
40
30
38
22
52
44
42
55
One of the ways to analyze data like that given in the table above is to make a scatter plot. To
make a scatter plot, you simply plot points on a Cartesian Coordinate system that is designed to
fit the data that you are analyzing.
Scatter Plot
Create a scatter plot of the data in the above table by plotting the points neatly on the grid
provided below.
60
Speed
(words per
minute)
40
20
0
0
5
10
15
Experience
(weeks)
Complete the following based on your scatter plot.
1. Do your points fall on a straight line?
2. Do your points appear to approximately follow a straight line?
Linear Function Notes
Page #9
Algebra
Notes: Linear Functions
Find the Equation of the Line
Finding The Equation of the Line of Best Fit on the Graphing Calculator
See separate handout for scatterplot directions.
Analysis
1. Predict the keyboarding speed of a student who has 15 weeks of experience.
2. Predict how many weeks of keyboarding experience a student would need in order to
type 100 words per minute.
Linear Function Notes
Page #10
Algebra
Notes: Linear Functions
Problem #1
A bookstore sold 576 copies of dictionaries in 1994 and 792 copies in 2002. Write an equation
that gives the number of copies sold in terms of the year.
Problem #2
Each month, a cell phone company charges a $10.50 plus $.03 per minute of use. Write an
equation that describes the total monthly bill for using that company’s services in terms of the
number of minutes used.
Problem #3
Between 1985 and 1995, the number of vacation trips in the United States taken by United States
residents was increasing by about 26 million per year. In 1993, United States residents went on
740 million vacation trips within the United States. Write an equation that describes the number
of vacation trips taken in the U.S. by U.S. residents in terms of the year.
Linear Function Notes
Page #11
Algebra
Notes: Linear Functions
Standard Form
A linear equation is in standard form when it looks like:
To be in standard form, A, B, and C must be …
The Standard Form Shortcut for graphing
If the equation of a line is in standard form, we can graph the line by making a “mini” table of
values.
1
0
Graph 3x – 4y = 24
x
y
1
0
1
0
1
0
Linear Function Notes
Page #12