1. Dependent v. Independent Variables
What’s the difference?

2. Bellwork
Complete task Unit 4 Lesson 2 Task #2 on Page 5 in your workbook.
This will be graded for as a classwork grade at the end of the unit.

3. Objective Distinguish between independent and dependent variables
Find the rate of change between two variables

4. Variables and Constants?
What is the difference between a variable and a constant
Variable
Constant

5. Independent Variables
What is controlled
Represented by x
Cause
Time is generally independent

6. Dependent Variables Determined by the independent variable Outcome
Effect
Represented by y

7. Examples: Which is independent or dependent
Cost and Minutes on Cell Phone
Hours studied and Grade on Exam
Income and education
Grade on exam and hours played video games
Salary and years worked
Age and height
Salary and hours worked
Other Examples

8. You Try Work in groups of 2’s
Complete Unit 4 Lesson 2 Task #3 on pages 6 & 7
This will be graded at the end of the unit as a classwork grade

9. Rate of Change
Rate of Change measures the change in the dependent variable over the change in the independent variable
It is synonymous with slope

10. Examples of where ROC is used
Real Estate
Finances
Sports

11. Recall the slope formula

12. To Find Rate of Change Identify the independent variable, x
Identify the dependent variable, y
Write two sets of ordered pairs
Find the slope
Determine the meaning of the slope

13. Example
The speed of sound travels 6 miles in 30 seconds and 10 miles in 50 seconds. Find the average rate of change.
What is the independent variable?
Time (seconds)
What is the dependent variable?
Distance (miles)
Write as a set of ordered pairs?
(30, 6) and (50, 10)
Find the slope?
Interpret the slope:
Speed of light travels 1 mile every 5 seconds

14. Example
Jeremy had 5 gallons of gas in his motorcycle. After driving 100 miles he had 3 gallons left.
What is the independent variable?
Gallons of gas
What is the dependent variable?
Distance (miles)
Write as a set of ordered pairs?
(5, 0) and (3, 100)
Find the slope?
Interpret the slope:
Every 50 miles traveled the tank drops one gallon

15. Example
A house valued at $225,000 pays $ in real estate taxes. A house valued at $750,000 pays $6,750 in taxes.
What is the independent variable?
Value of the home
What is the dependent variable?
Real estate taxes
Write as a set of ordered pairs?
(225,000, ) and (750,000, 6,750)
Find the slope?
Interpret the slope:
You pay $9 for every $1000 your home is worth

16. Example 1. You drive 30 miles in one hour and 120 miles in four hours.
What is the independent variable?
Time (hours)
What is the dependent variable?
Distance (miles)
Write as a set of ordered pairs?
(1, 30), (4, 120)
Find the slope?
Interpret the slope:
You drive 30 miles every 1 hour

17. Example
2. The cost of a group museum tickets is $48 for four people and $78 for ten people.
What is the independent variable?
# of people
What is the dependent variable?
Cost ($)
Write as a set of ordered pairs?
(4, 48), (10, 78)
Find the slope?
Interpret the slope:
Every one person pays $5.00

18. You Try Locker Bay Time Again
Get with a partner. Complete page 4. One complete the even’s the other completes the odd’s
You have 15 minutes.
No phones, staying on task, gets you SER points!
Pop Quiz when we are done!

19. X-Y Intercepts (page 12)

20. Objective Find x- and y-intercepts
Use x and y intercepts to graph a line

21. How to find To find the x-intercept, set y = 0
To find the y-intercept, set x = 0

22. Find the x-y-intercepts and graph
To find the x-intercept, make y = 0
Solve for x (divide by 4)
The x intercept is

23. Find the x-y-intercepts and graph
To find the y-intercept, make x = 0
Solve for y
The y intercept is

24. Graph: 4x + y = 5
x-intercept is (1.25, 0)
y-intercept is (0, 5)

25. Classwork In groups of 2, complete Unit 4 Lesson 2 Task #4 on page 8
This will be graded as classwork activity at the end of this unit

26. Find the x-y-intercepts and graph
To find the x-intercept, make y = 0
Solve for x (divide by 4)
x-int: (1, 0)
To find the y-intercept,
Make x = 0
y-int: (0, -1)

27. Graph: x – y = 1
x-intercept is (1, 0)
y-intercept is (0, -1)

28. Find the x-y-intercepts and graph
To find the x-intercept, make y = 0
Solve for x (divide by 4)
x-int: (8, 0)
To find the y-intercept,
Make x = 0
y-int: (0, 2)

29. Graph: x + 4y = 8
x-intercept is (8,0)
y-intercept is (0, 2)

30. Complete page 12.