Algebraic Representations and Rates of Change

The video tutorial explains how to calculate the constant rate of change in a linear function using four representations: verbal, algebraic, numeric, and graphical. It highlights common mistakes, such as incorrect sign for slope, and demonstrates how to identify the rate of change from different representations. The lesson includes a practice problem to reinforce understanding.

What is the constant rate of change in the pool example?

• -350 gallons per hour

• 350 gallons per hour

• 0 gallons per hour

• 1400 gallons per hour

What is a common mistake when calculating the slope?

• Using addition instead of subtraction

• Incorrect order of subtraction

• Ignoring the x-values

• Multiplying instead of dividing

In the pool example, what does the keyword 'emptied' indicate?

• A positive rate of change

• A constant rate of change

• A negative rate of change

• No change

What is the algebraic representation of the pool problem?

• W = 350T - 1400

• W = 1400T - 350

• W = 350T + 1400

• W = -350T + 1400

How is the constant rate of change identified in a numeric representation?

• By multiplying the x and y values

• By dividing the change in y by the change in x

• By subtracting the x-values

• By adding the y-values

In the graphical representation, what are the coordinates of the two points used?

• (0, 1400) and (2, 700)

• (1, 1050) and (3, 350)

• (0, 1400) and (1, 1050)

• (0, 700) and (2, 1400)

What is the constant rate of change in the bicycle example?

• $5 per hour

• $30 per hour

• $60 per hour

• $6 per hour

What is the algebraic equation for the bicycle example?

• Y = 60X - 6

• Y = 6X + 60

• Y = 6X - 60

• Y = 60X + 6

In the bicycle example, how much does William earn after 5 hours?

• $30

• $60

• $0

• $90

What is the graphical representation of the bicycle example?

• Starts at -$30 and ends at $60

• Starts at $60 and ends at $0

• Starts at -$60 and ends at -$30

• Starts at $0 and ends at $60