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Dependent v. Independent Variables

Dependent v. Independent Variables. What’s the difference?. 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. Objective. Distinguish between independent and dependent variables

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Dependent v. Independent Variables

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  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 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 The speed of sound travels 6 miles in 30 seconds and 10 miles in 50 seconds. Find the average rate of change.

  14. Example 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 Jeremy had 5 gallons of gas in his motorcycle. After driving 100 miles he had 3 gallons left.

  15. Example 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, 2020.50) and (750,000, 6,750) Find the slope? Interpret the slope: You pay $9 for every $1000 your home is worth A house valued at $225,000 pays $2020.50 in real estate taxes. A house valued at $750,000 pays $6,750 in taxes.

  16. Example 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 1. You drive 30 miles in one hour and 120 miles in four hours.

  17. Example 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 2. The cost of a group museum tickets is $48 for four people and $78 for ten people.

  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 • 4x + y = 5 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 • 4x + y = 5 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 2. x – y = 1 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 3. x + 4y = 8 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.

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