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 Find the rate of change between two variables

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

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

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

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

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

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

Examples of where ROC is used Real Estate Finances Sports

Recall the slope formula  

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

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

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

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

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

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

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!

X-Y Intercepts (page 12)

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

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

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

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

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

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

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)

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

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)

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

Complete page 12.