Unit 3 Notes – Modelling Graphs (Chapter 5 in Textbook)

Day Date Classwork Assignment Checklist

1 Thurs. Oct. 6 Test #2 Watch Video #3.1 –

Direct Variation P.S. #3.1 ________

P.S. #3.2 ________

P.S. #3.3 ________

P.S. #3.4 ________

P.S. #3.5 ________

P.S. #3.6 ________

Review #3 ________

Total:

_______________

2 Fri.

Oct. 7 Direct Variation Watch Video #3.2 – Partial Variation

3 Tues.

Oct. 11 Partial Variation Watch Video #3.3 – Slope

4 Wed.

Oct. 12 Slope Watch Video #3.4 – Slope as a Rate of Change

5 Thurs. Oct. 13 Slope as a Rate of Change Watch Video #3.5 – First

Differences

6 Mon.

Oct. 17 First Differences Finish First Differences/Catch up on Checklist

7 Tues.

Oct. 18 Quiz Watch Video #3.6 –Variation, Slope, and First Differences

8 Wed.

Oct. 19 Variation, Slope, and First

Differences Finish Checklist

9 Thurs. Oct. 20 Review for Test #3 Review for Test #3A

10 Fri.

Oct. 21 Review Game Review for Test #3B

11 Mon.

Oct. 24 Test #3 Watch Video #4.1

Name: ________________________________________________________________________

Unit 3 Notes – MPM1D Modelling with Graphs 3

1.) If you leave home and walk in a given direction at a steady pace, your distance, d feet, from

home directly varies with the time, x minutes, you walk. You can use a table and a graph to represent this proportional relationship.

Time (x minutes) 1 2 3 4 5

Distance from Home (d feet) 250 500

a.) Fill in the rest of the chart. b.) What is the constant of proportionality?

c.) Graph the information given in the chart.

d.) Using riserun

, find the slope of the line.

2.) Think of examples in which you would require rates of change.

Unit 3 Notes – MPM1D Modelling with Graphs 4

3.) The graphs give information about a penguin’s number of heartbeats, b, over time, t minutes, during normal resting and just before diving. When is the penguin’s heart rate greater, during normal resting, or just before diving?

4.) The graphs give information about the distance, d miles, traveled over time, t hours, by cars and trucks on a California highway. Which speed is lower?

Direct Variation:

Unit 3 Notes – MPM1D Modelling with Graphs 5

1.) A taxi costs $2 for the initial meter fare and $0.50 for each additional kilometer.

a. Define variables to represent the unknowns in the problem. Identify the independent and dependent variables.

b. Write an equation to represent this situation.

c. Create a chart to represent this situation.

d. Create a graph to represent this situation.

e. This is an example of partial variation. What do you think partial variation means?

Unit 3 Notes – MPM1D Modelling with Graphs 6

Partial Variation:

2.) Take a look at the table of values shown to the right. a. Find the missing values that will allow y to vary partially with x. b. Identify the initial value of y and the constant of variation.

c. Write an equation relating y and x in the form y = mx + b.

d. Graph this relation.

x y 0 6 1 9 2 3 15 4 27

Unit 3 Notes – MPM1D Modelling with Graphs 7

Notes 3.3 – Slope 1.) Graph the line below on graph paper. The line should pass through the points (0,1) and

(6,4). Then draw and label three right triangles on the line as shown. The triangles should be the same shape but different sizes. Make sure that each right angle lies on the intersection of two gridlines.

2.) Complete the table.

Triangle Length of Vertical

Side Length of Horizontal

Side

A

B

C

3.) What do you notice about the last column of the table?

Slope Formula:

Unit 3 Notes – MPM1D Modelling with Graphs 8

Find the slope of each line. 1.) 2.) 3.) 4.) 5.) When will the slope of a line be positive? Negative?

6.) Determine the slope of the line that passes through (2,-5) and (7,-10).

7.) Determine the slope of the line that passes through (-5,7) and (-5,9).

8.) Determine the slope of the line that passes through (-7,8) and (-9,8).

Unit 3 Notes – MPM1D Modelling with Graphs 9

Notes 3.4 – Slope as a Rate of Change 1.) The graph shows the volume of gasoline remaining in a car’s tank.

a.) Calculate the slope of the graph.

b.) Interpret the slope as a rate of change.

c.) Write an equation to represent the situation. Interpret the equation.

d.) Use the equation to determine how many liters are left in the tank when the car travels 300 km. Is this answer supported by the graph?

2.) Aaliyah and Emily are riding the bus. There is a fee to use the bus and an additional rate per mile. Aaliyah goes 5 miles and pays $7. Emily goes 9 miles and pays $10.20. How much is the rate per mile?

3.) Katie and Sarah join a gym. The gym has a joining fee and a monthly rate. Katie goes for 8 months and pays $262. Sarah goes for 11 months and pays $349. How much is the monthly rate?

*A rate of change requires _____________ and compares _____________ _____________.

Unit 3 Notes – MPM1D Modelling with Graphs 10

Notes 3.5 – First Differences 1.) Consider the relation y = 3x – 4.

a.) Complete the table of values.

b.) Graph the relation. c.) Is this relation linear or non-linear?

d.) Find the first differences. What conclusion can you make about the first differences?

2.) Use first differences to determine which of these relations are linear and which are non-linear.

x y

Unit 3 Notes – MPM1D Modelling with Graphs 11

Notes 3.6 – Connecting Variation, Slope, and First Differences The Rule of Four

A mathematical relation can be represented in four different ways: 1.) ________________________________________________________________________2.) ________________________________________________________________________ 3.) ________________________________________________________________________ 4.) ________________________________________________________________________

1.) Scenario #1

In Words

A cable car starts at a height of 700 feet and is descending at a rate of 30 feet per minute.

In a Table

In a Graph

In an Equation

Unit 3 Notes – MPM1D Modelling with Graphs 12

2.) Scenario #2

In Words

In a Table Time (hr) Cost ($)

0 40

1 55

2 70

3 85

In a Graph

In an Equation

3.) Scenario #3

In Words

In a Table

In a Graph

In an Equation