1. LINEAR RELATIONS
CHAPTER 4

2. Writing Equations to Describe Patterns
4.1
Bring Graph Paper Next Class!

3. Page 154; Move Desks to Match Problem

4. Example 1
Is she right?
Number of Hexagons
Number of Match Sticks

5. Example 2
Write a linear expression for the following: a)

6. Example 2
Write a linear expression for the following: b) 1, 4, 7, 10, 13
Term
Number

7. Example 3 $5 Dollars to Enter $2 per Ride
Teagan goes to a carnival. The cost for a ride is shown on a poster at the entrance. a) Write an equation that relates the total cost, C dollars, to the number of rides, r.
$5 Dollars to Enter
$2 per Ride

8. Example 3 $5 Dollars to Enter $2 per Ride
Teagan goes to a carnival. The cost for a ride is shown on a poster at the entrance. b) Teagan goes on 4 rides. What is his total cost?
$5 Dollars to Enter
$2 per Ride

9. Example 4 Number of Toppings, n Cost of Pizza, C $
A pizza with tomato sauce and cheese cost $ Each additional topping costs $0.75.
Create a table that shows the costs of a pizza for up to 5 toppings.
Write an equation to represent this example.
Number of Toppings, n
Cost of Pizza, C $

10. Example 4
A pizza with tomato sauce and cheese cost $ Each additional topping costs $0.75.
b) If the cost of the pizza is $15, how many topping are on it?

11. Example 5
An airplane is cruising at a height of m. It descends to land. This table shows the height of the plane every minute after it began its descent. The height of the plane changes at a constant rate. a) Write an equation for the height of the plane to the time since it began its descent.

12. Example 5
An airplane is cruising at a height of m. It descends to land. This table shows the height of the plane every minute after it began its descent. The height of the plane changes at a constant rate. A) h = – 300t b) What is the height of the plane after 15 min?

13. Example 5
An airplane is cruising at a height of m. It descends to land. This table shows the height of the plane every minute after it began its descent. The height of the plane changes at a constant rate. b) h = – 300t c) How long after the beginning its descent does the plane land?

14. Linear Relations
4.2
Quiz Coming Soon

15. Review
A local phone company offer a cell phone plan that has a fixed cost per month and a cost related to the number of text messages sent. The fixed cost is $20 and each message sent cost 10 cents.
Create a table showing the relationship.
Create an equation where c is the cost and n is the number of messages.
In your own words, describe the relationship.

16. Review Number of Messages Cost ($)
A local phone company offer a cell phone plan that has a fixed cost per month and a cost related to the number of text messages sent. The fixed cost is $20 and each message sent cost 10 cents.
Create a table showing the relationship.
Create an equation where c is the cost and n is the number of messages.
In your own words, describe the relationship.
Number of Messages
Cost ($)

17. Example 1
Graph the cost of the cell phone plan.

18. Four Ways to Express Data
_____________

19. Example 2 – Do you Remember these?
Above is a table that expresses how much it costs to rent a movie.
Graph the data
Create an Equation
Number of Movies Rented
Cost ($) 1
3.50 2
7.00 3
10.50 4
14.00

20. Number of Movies Rented
Example 2
Number of Movies Rented
Cost ($) 1
3.50 2
7.00 3
10.50 4
14.00
Graph the data

21. Number of Movies Rented
Example 2
Create an Equation
Number of Movies Rented
Cost ($) 1
3.50 2
7.00 3
10.50 4
14.00

22. Graphing
What do you notice about both graphs? Do all graphs look this way? What would an equation look like that would give a different looking graph?

23. Definition
Linear Relation – When the graph of the relation is a ___________ line, we have a ____________ relation. In a linear relation, a ___________ change in one quantity produces a constant change in the related quantity. Ie. The graphs are straight lines

24. Number of Movies Rented
Variables
Which one is the independent variable? Dependent Variable? Does it matter?
Number of Movies Rented
Cost ($) 1
3.50 2
7.00 3
10.50 4
14.00

25. Definitions
Independent variable – what we are _______________ Dependent Variable – what changes in ________________ to our change Always graph the independent variable on the horizontal axis, and the dependent variable on the vertical axis.

26. Checking if Linear without a Graph

27. Example 3 A relation has the equation y = 6 – 3x
Create a table of values from -3 to 3
Graph the relation
Is this linear?
Describe in words (when x increases by one, y…)

28. Example 3 A relation has the equation y = 6 – 3x
Create a table of values from -3 to 3
X (Input)
Y (Output)

29. c) Is it Linear? d) Describe in Words Example 3
X (Input)
Y (Output) -3 15 -2 12 -1 9 6 1 3 2
A relation has the equation y = 6 – 3x
b) Graph the relation
c) Is it Linear?
d) Describe in Words

30. Example 4 A relation has the equation y = 2x + 4
Create a table of values from -3 to 3
Graph the relation
Is this linear?
Describe in words (when x increases by one, y…)

31. c) Is it Linear? d) Describe in Words Example 4
X (Input)
Y (Output)
A relation has the equation y = 2x + 4
b) Graph the relation
c) Is it Linear?
d) Describe in Words

32. Another Form of the Equation for a Linear Relation
4.3
Quiz Coming Soon!

33. Review A relation has the equation x + y = 3
Create a table of values from -3 to 3
Graph the relation
Is this linear?
Describe in words (when x increases by one, y…)

34. c) Is it Linear? d) Describe in Words Review
X (Input)
Y (Output)
A relation has the equation x + y = 3
b) Graph the relation
c) Is it Linear?
d) Describe in Words

35. Example 1
For each equation create a table with 3 x-values, then graph. a) x = -4
X (Input)
Y (Output)

36. Example 1
For each equation create a table with 3 x-values, then graph. b) y +2 = 0
X (Input)
Y (Output)

37. Example 1
For each equation create a table with 3 x-values, then graph. c) 2x = 5
X (Input)
Y (Output)

38. Concept

39. Example 2 A relation has the equation 3x - 2y = 6
Create a table of values for x = -4, 0, and 4
Graph the relation
Is this linear?
Describe in words (when x increases by one, y…)

40. c) Is it Linear? d) Describe in Words Example 2
A relation has the equation 3x – 2y =6
b) Graph the relation
c) Is it Linear?
d) Describe in Words
X (Input)
Y (Output)

41. Example 3 A relation has the equation 1 = 2x + y
Create a table of values for x = -4, 0, and 4
Graph the relation
Is this linear?
Describe in words (when x increases by one, y…)

42. c) Is it Linear? d) Describe in Words Example 3
A relation has the equation 1 = 2x + y
b) Graph the relation
c) Is it Linear?
d) Describe in Words
X (Input)
Y (Output)

43. Review
Study Guide Determine expressions from problems - Express data in four different ways: - Table, graph, words and expression - For graph you must have: axis labels with units, title - Use expressions to solve problems