Linear Functions and Rate of Change

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 that in the equation y = mx + b, the rate of change is the slope (m), and the initial value is the y-intercept (b). The lesson includes an example involving baseball card resale values, demonstrating how to identify increasing or decreasing values and comparing rates of change. 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 y-intercept

• The rate of change

• The initial value

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

• The function is increasing

• The function is constant

• The function is decreasing

• The function is undefined

What is the significance of a negative rate of change in a linear function?

• The function is constant

• The function is decreasing

• The function is increasing

• The function is undefined

What is the initial value in the equation y = mx + b?

• The rate of change

• The value of x when y is zero

• The slope of the line

• The value of y when x is zero

In the baseball card case study, what does the equation y = 5 - 0.7x represent for card A?

• The card's value remains constant

• The card's value increases by 70 cents each year

• The card's initial value is 70 dollars

• The card's value decreases by 70 cents each year

Which cards are decreasing in value each year?

• Card A and Card B

• Card C and Card D

• Card B and Card C

• Card A and Card D

Which cards had the greatest initial values at purchase?

• Card B and Card C

• Card A and Card D

• Card C and Card D

• Card A and Card B

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

• Card B

• Card A

• Card C

• Card D

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 A

• Card B

• Card D

• Card C

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

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

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

• Card C's initial value is 90 dollars

• Card C's value remains constant