1. Click the mouse button or press the Space Bar to display the answers.
Transparency 6

2. Splash Screen

3. Graph linear equations
Objective
Graph linear equations
Example 6-3c

4. A relationship where one thing depends on another
Vocabulary
Function
A relationship where one thing depends on another
Example 6-3c

5. Vocabulary Function table
An organized method of the input numbers, output numbers, and the function rule
Input
Function
Output
Domain
Rule
Range
Example 6-3c

6. Vocabulary Domain The set of input values
Example 6-3c

7. The set of output values
Vocabulary
Range
The set of output values
Example 6-3c

8. An equation, when graphed, forms a straight line
Vocabulary
Linear equation
An equation, when graphed, forms a straight line
Example 6-3c

9. A pair of numbers used to locate a point in a coordinate system
Review Vocabulary
Ordered pair
A pair of numbers used to locate a point in a coordinate system
Example 6-3c

10. Example 1 Make a Function Table
Example 2 Graph Solutions of Linear Equations
Example 3 Represent Real-World Functions
Lesson 6 Contents

11. WORK Asha makes $6. 00 an hour working at a grocery store
WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours.
Make a function table
Label columns
Input
Function
Output
1/3
Example 6-1a

12. $6.00 an hour total earnings hours
WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours.
$6.00 an hour
total
earnings
hours
Identify the input
Identify the function
Identify the function
Input
Function
Output
Total Earnings ($)
Number of Hours
Multiply by 6
1/3
Example 6-1a

13. Put number of hours in the input column
WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours.
hours
Put number of hours in the input column
Input
Function
Output
Total Earnings ($)
Number of Hours
Multiply by 6 1 2 3 4
1/3
Example 6-1a

14. Multiply the input by 6 to find the output
WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours.
Multiply the input by 6 to find the output
Input
Function
Output
Total Earnings ($)
Number of Hours
Multiply by 6 1
1  6 6 2
2  6 12 3
3  6 18 4
4  6 24
1/3
Example 6-1a

15. WORK Asha makes $6. 00 an hour working at a grocery store
WORK Asha makes $6.00 an hour working at a grocery store. Make a function table that shows Asha’a total earnings for working 1, 2, 3, and 4 hours.
Answer:
Input
Function
Output
Total Earnings ($)
Number of Hours
Multiply by 6 1
1  6 6 2
2  6 12 3
3  6 18 4
4  6 24
1/3
Example 6-1a

16. MOVIE RENTAL Dave goes to the video store to rent a movie
MOVIE RENTAL Dave goes to the video store to rent a movie. The cost per movie is $3.50. Make a function table that shows the amount Dave would pay for renting 1, 2, 3, and 4 movies.
Answer:
Input
Function Rule
Output
Number of Movies
Multiply by 3.50
Total Cost ($) 1
3.50  1
3.50 2
3.50  2
7.00 3
3.50  3
10.50 4
3.50  4
14.00
1/3
Example 6-1b

17. Make a table with 4 columns
Label 1st column as “x”
Graph
Label 2nd column with the rule
Label 3rd column as “y” x
x + 3 y
2/3
Make a table with an x column, a rule column, a y column, and an ordered pair column
Example 6-2a

18. Label 4th column as the ordered pairs (x, y)
Graph
Select any four values for the input x
I choose 2, 1, 0, and -1 because they are small and easy x
x + 3 y
(x, y) 2
2 + 3 5
(2, 5)
Substitute the value of x into the function column 1
1 + 3 4
(1, 4)
Make the ordered pairs from the x and y columns
0 + 3 3
(0, 3) -1
-1 + 3 2
(-1, 2)
2/3
Example 6-2a

19. Graph the ordered pairs Label ordered pairs
(2, 5)
Graph
(1, 4)
Graph the ordered pairs
(0, 3)
Label ordered pairs
(–1, 2) x
x + 3 y
(x, y) 2
2 + 3 5
(2, 5) 1
1 + 3 4
(1, 4) 3
0 + 3
(0, 3) -1
-1 + 3 2
(-1, 2)
2/3
Example 6-2a

20. Draw a line connecting the dots
(2, 5)
Graph
(1, 4)
Draw a line connecting the dots
(0, 3)
(–1, 2) x
x + 3 y
(x, y) 2
2 + 3 5
(2, 5) 1
1 + 3 4
(1, 4)
0 + 3 3
(0, 3) -1
-1 + 3 2
(-1, 2)
2/3
Example 6-2a

21. Graph Answer: x x + 3 y (x, y) 2 2 + 3 5 (2, 5) 1 1 + 3 4 (1, 4) 0 + 3
(0, 3)
(–1, 2) x
x + 3 y
(x, y) 2
2 + 3 5
(2, 5) 1
1 + 3 4
(1, 4)
0 + 3 3
(0, 3) -1
-1 + 3 2
(-1, 2)
2/3
Example 6-2a

22. Ordered pairs will vary depending on your choice for x but the line should be alike
Graph
Answer:
2/3
Example 6-2b

23. Draw a function table with 4 columns t 30t d
ANIMALS Blue whales can reach a speed of 30 miles per hour in bursts when in danger. The equation describes the distance d that a whale traveling at that speed can travel in time t. Represent this function with a graph.
Draw a function table with 4 columns t
30t d
Label the 1st column with t for time
Label the 2nd column with the rule
Label the 3rd column with the output for distance d
3/3
Example 6-3a

24. Label 4th column with the ordered pairs t 30t d (t, d)
ANIMALS Blue whales can reach a speed of 30 miles per hour in bursts when in danger. The equation describes the distance d that a whale traveling at that speed can travel in time t. Represent this function with a graph.
Label 4th column with the ordered pairs t
30t d
(t, d) 1
Choose 4 values for the time 2
I choose 1, 2, 3, and 4 hours because they are easy to graph 3 4
3/3
Example 6-3a

25. Substitute the input of t into the function t 30t d (t, d)
ANIMALS Blue whales can reach a speed of 30 miles per hour in bursts when in danger. The equation describes the distance d that a whale traveling at that speed can travel in time t. Represent this function with a graph.
Substitute the input of t into the function t
30t d
(t, d) 1
30  1 30
(1, 30)
Find the output d
Make ordered pairs from the t and d columns 2
30  2 60
(2, 60) 3
30  3 90
(3, 90) 4
30  4
120
(4, 120)
3/3
Example 6-3a

26. Graph the ordered pairs
Label the horizontal axis
Label the vertical axis
140
120
Scale must include
100 80 t
30t d
(t, d) 1
30(1) 30
(1, 30) 2
30(2) 60
(2, 60) 3
30(3) 90
(3, 90) 4
30(4)
120
(4, 120) 60 40 20 1 2 3 4
3/3
Example 6-3a

27. Draw a line through the points 140
Plot each ordered pair
Draw a line through the points
140
(4, 120)
120
Answer:
100
(3, 90) 80 t
30t d
(t, d) 1
30(1) 30
(1, 30) 2
30(2) 60
(2, 60) 3
30(3) 90
(3, 90) 4
30(4)
120
(4, 120) 60
(2, 60) 40
(1, 30) 20 1 2 3 4
3/3
Example 6-3a

28. *
TRAVEL Susie takes a car trip traveling at an average speed of 55 miles per hour. The equation describes the distance d that Susie travels in time t. Represent this function with a graph.
Answer:
3/3
Example 6-3c

29. Functions and Linear Equations
Assignment
Lesson 4:6
Functions and Linear Equations
All
End of Lesson 6