Linear Functions and Card Values

This video tutorial for Grade 8 Module 6 Lesson 2 covers linear functions, focusing on interpreting the rate of change and initial value. It explains how to identify these components in the equation y = mx + b, where m is the rate of change and b is the initial value. The lesson includes an example involving the resale values of baseball cards, demonstrating how to analyze and interpret linear equations. The video concludes with a Q&A session addressing specific questions about the example.

What does the 'm' represent in the linear equation y = mx + b?

• The x-intercept

• The constant term

• The slope or rate of change

• The y-intercept

If a linear function has a negative rate of change, what does this indicate about the function?

• The function is undefined

• The function is decreasing

• The function is increasing

• The function is constant

What is the initial value of a linear function?

• The value of y when x is zero

• The slope of the line

• The rate of change

• The value of x when y is zero

What is the significance of the initial value in a linear function?

• It is the value of x when y is zero

• It indicates the rate of change

• It is the value of y when x is zero

• It determines the slope of the line

In the baseball card example, what does the equation y = 5 - 0.7x tell us about card A?

• Card A's value increases by 70 cents each year

• Card A's initial value is $5

• Card A's value decreases by 70 cents each year

• Card A's initial value is $0.7

Which cards are decreasing in value each year?

• Card B and Card C

• Card C and Card D

• Card A and Card B

• Card A and Card D

Which cards had the greatest initial values at purchase?

• Card A and Card B

• Card C and Card D

• Card A and Card D

• Card B and Card C

Which card is increasing in value the fastest from year to year?

• Card B

• Card D

• Card C

• Card A

If you were to graph the equations of the resale values of card B and card C, which card's graph line would be steeper?

• Card C

• Card D

• Card A

• Card B

What does the 0.9 value in the card C equation represent?

• Card C's value remains constant

• Card C's value increases by 90 cents per year

• Card C's initial value is $0.9

• Card C's value decreases by 90 cents per year