Understanding Rates of Change in Carpet Cleaning Costs

This video tutorial introduces the concept of using rates of change to build tables and graphs. It provides an example of calculating costs for a carpet cleaning service, where the rate of change is the cost per room and the starting value is a reservation fee. The tutorial guides viewers through completing a table of costs based on the number of rooms cleaned and plotting these costs on a graph. It concludes with a discussion on why the graph should not connect data points and presents an equation to represent the cost calculation.

What is the primary focus of the lesson introduced in the video?

• Using rates of change to build tables and graphs

• Understanding algebraic expressions

• Learning about geometric shapes

• Studying historical events

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

In the carpet cleaning example, what is the rate of change?

• $25 reservation fee

• $40 total cost

• $55 for two rooms

• $15 per room cleaned

Tags

CCSS.HSF.LE.B.5

What is the starting value in the carpet cleaning cost scenario?

• $15 per room

• $25 reservation fee

• $40 for one room

• $55 for two rooms

Tags

CCSS.HSF.LE.B.5

How much does the total cost increase when one additional room is cleaned?

• $10

• $20

• $15

• $25

What is the total cost for cleaning three rooms?

• $100

• $85

• $70

• $55

Tags

CCSS.8.EE.B.5

What is the first ordered pair for graphing the cost data?

• (2, 55)

• (0, 25)

• (3, 70)

• (1, 40)

How should the horizontal axis be scaled for the graph?

• By 1s

• By 10s

• By 2s

• By 5s

Tags

CCSS.8.EE.B.5

Why does it not make sense to connect the data points on the graph?

• The data points are not related

• The graph is already complete

• The number of rooms cleaned must be a whole number

• The data points are too close together

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

What is the equation used to calculate the total cost based on the number of rooms cleaned?

• C(x) = 20 + 15x

• C(x) = 30 + 15x

• C(x) = 25 + 15x

• C(x) = 25 + 10x

Tags

CCSS.HSF.LE.B.5

What must be true about the variable X in the cost equation?

• X can be any real number

• X must be a whole number

• X can be a fraction

• X must be negative

Tags

CCSS.HSF.LE.B.5