Gr.8 M6 L2

In 2008, a collector of sports memorabilia purchased 5 specific baseball cards as an investment. Let 𝑦 represent each card’s resale value (in dollars) and 𝑥 represent the number of years since purchase. Each card’s resale value after 0, 1, 2, 3, and 4 years could be modeled by linear equations as follows:

Card A: 𝑦 = 5− 0.7𝑥

Card B: 𝑦 = 4+ 2.6𝑥

Card C: 𝑦 = 10+ 0.9𝑥

Card D: 𝑦 = 10− 1.1𝑥

Card E: 𝑦 = 8+ 0.25𝑥

Which card(s) are decreasing in value each year? How can you tell?

• Card A

• Card B

• Card C

• Card D

• Card E

In 2008, a collector of sports memorabilia purchased 5 specific baseball cards as an investment. Let 𝑦 represent each card’s resale value (in dollars) and 𝑥 represent the number of years since purchase. Each card’s resale value after 0, 1, 2, 3, and 4 years could be modeled by linear equations as follows:

Card A: 𝑦 = 5− 0.7𝑥

Card B: 𝑦 = 4+ 2.6𝑥

Card C: 𝑦 = 10+ 0.9𝑥

Card D: 𝑦 = 10− 1.1𝑥

Card E: 𝑦 = 8+ 0.25𝑥

Which card(s) had the greatest initial value at purchase (at 𝟎 years)?

• Card A

• Card B

• Card C

• Card D

• Card E

In 2008, a collector of sports memorabilia purchased 5 specific baseball cards as an investment. Let 𝑦 represent each card’s resale value (in dollars) and 𝑥 represent the number of years since purchase. Each card’s resale value after 0, 1, 2, 3, and 4 years could be modeled by linear equations as follows:

Card A: 𝑦 = 5− 0.7𝑥

Card B: 𝑦 = 4+ 2.6𝑥

Card C: 𝑦 = 10+ 0.9𝑥

Card D: 𝑦 = 10− 1.1𝑥

Card E: 𝑦 = 8+ 0.25𝑥

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

• Card A

• Card B

• Card C

• Card D

• Card E

In 2008, a collector of sports memorabilia purchased 5 specific baseball cards as an investment. Let 𝑦 represent each card’s resale value (in dollars) and 𝑥 represent the number of years since purchase. Each card’s resale value after 0, 1, 2, 3, and 4 years could be modeled by linear equations as follows:

Card A: 𝑦 = 5− 0.7𝑥

Card B: 𝑦 = 4+ 2.6𝑥

Card C: 𝑦 = 10+ 0.9𝑥

Card D: 𝑦 = 10− 1.1𝑥

Card E: 𝑦 = 8+ 0.25𝑥

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 C

• Card D

• Card E

In 2008, a collector of sports memorabilia purchased 5 specific baseball cards as an investment. Let 𝑦 represent each card’s resale value (in dollars) and 𝑥 represent the number of years since purchase. Each card’s resale value after 0, 1, 2, 3, and 4 years could be modeled by linear equations as follows:

Card A: 𝑦 = 5− 0.7𝑥

Card B: 𝑦 = 4+ 2.6𝑥

Card C: 𝑦 = 10+ 0.9𝑥

Card D: 𝑦 = 10− 1.1𝑥

Card E: 𝑦 = 8+ 0.25𝑥

Write a sentence explaining the 𝟎. 𝟗 value in Card C’s equation.

• The 𝟎.𝟗 value means that Card C’s value increases by 𝟗𝟎 cents per year

• The 𝟎.𝟗 value means that Card C’s value increases by 𝟗 cents per year

• The 𝟎.𝟗 value means that Card C’s value increases by 𝟗 percents per year

• The 𝟎. 𝟗 value means that Card C’s value increases by 𝟗𝟎 percent per year

A rental car company offers the following two pricing methods for its customers to choose from for a one-month rental:

Method 1: Pay $𝟒𝟎𝟎 for the month, or

Method 2: Pay $𝟎. 𝟑𝟎 per mile plus a standard maintenance fee of $𝟑𝟓.

a. Construct a linear function that models the relationship between the miles driven and the total rental cost for Method 2. Let 𝒙 represent the number of miles driven and 𝒚 represent the rental cost (in dollars).

• 𝒚 = 𝟑𝟓 + 𝟎. 𝟑𝟎𝒙

• 𝒚 = 𝟎. 𝟑𝟎 + 𝟑𝟓𝒙

• 𝒚 = 𝟑𝟓𝒙 + 𝟎. 𝟑𝟎

• 𝒚 = 𝟎. 𝟑𝟎𝒙 + 𝟑𝟓

A rental car company offers the following two pricing methods for its customers to choose from for a one-month rental:

Method 1: Pay $𝟒𝟎𝟎 for the month, or

Method 2: Pay $𝟎. 𝟑𝟎 per mile plus a standard maintenance fee of $𝟑𝟓.

If you plan to drive 𝟏, 𝟏𝟎𝟎 miles for the month, which method would you choose?

• Method 1 has a flat rate of $𝟒𝟎𝟎 regardless of miles

• Method 2, the cost would be $𝟑𝟔𝟓

• Both are the same

• Neither would be a good choice

Recall from a previous lesson that Kelly wants to add new music to her MP3 player. She was interested in a monthly subscription site that offered its MP3 downloading service for a monthly subscription fee plus a fee per song. The linear function that modeled the total monthly cost in dollars (𝒚) based on the number of songs downloaded (𝒙) is 𝒚 = 𝟓. 𝟐𝟓 + 𝟎. 𝟑𝟎𝒙.

The site has suddenly changed its monthly price structure. The linear function that models the new total monthly cost in dollars (𝒚) based on the number of songs downloaded (𝒙) is 𝒚 = 𝟎. 𝟑𝟓𝒙 + 𝟒. 𝟓𝟎.

If you were to graph the two equations (old versus new), which line would have the steeper slope?

• The old line would be steeper

• The new line would be steeper

• The two lines would have the same steepness

Recall from a previous lesson that Kelly wants to add new music to her MP3 player. She was interested in a monthly subscription site that offered its MP3 downloading service for a monthly subscription fee plus a fee per song. The linear function that modeled the total monthly cost in dollars (𝒚) based on the number of songs downloaded (𝒙) is 𝒚 = 𝟓. 𝟐𝟓 + 𝟎. 𝟑𝟎𝒙.

The site has suddenly changed its monthly price structure. The linear function that models the new total monthly cost in dollars (𝒚) based on the number of songs downloaded (𝒙) is 𝒚 = 𝟎. 𝟑𝟓𝒙 + 𝟒. 𝟓𝟎.

Which subscription plan provides the better value if Kelly downloads fewer than 𝟏𝟓 songs per month?

• The new plan is cheaper if Kelly downloads fewer than 𝟏𝟓 songs.

• The old plan is cheaper if Kelly downloads fewer than 𝟏𝟓 songs.

• Both plans are the same

• Neither plan would be cheaper

Recall from a previous lesson that Kelly wants to add new music to her MP3 player. She was interested in a monthly subscription site that offered its MP3 downloading service for a monthly subscription fee plus a fee per song. The linear function that modeled the total monthly cost in dollars (𝒚) based on the number of songs downloaded (𝒙) is 𝒚 = 𝟓. 𝟐𝟓 + 𝟎. 𝟑𝟎𝒙.

The site has suddenly changed its monthly price structure. The linear function that models the new total monthly cost in dollars (𝒚) based on the number of songs downloaded (𝒙) is 𝒚 = 𝟎. 𝟑𝟓𝒙 + 𝟒. 𝟓𝟎.

Explain the meaning of the value 𝟎. 𝟑𝟓 in the new equation. Is this a better situation for Kelly than before?

• The rate of change is 𝟎. 𝟑𝟓. This means that the cost is increasing by $𝟎. 𝟑𝟓 for every song downloaded. This is more than the download cost for the original plan.

• The rate of change is 𝟎. 𝟑𝟓. This means that the cost is decreasing by $𝟎. 𝟑𝟓 for every song downloaded. This is less than the download cost for the original plan.

• The rate of change is 𝟎. 𝟑𝟓. This means that the cost is increasing by $𝟎. 𝟑𝟓 for every song downloaded. This is less than the download cost for the original plan.

• The rate of change is 𝟎. 𝟑𝟓. This means that the cost is decreasing by $𝟎. 𝟑𝟓 for every song downloaded. This is more than the download cost for the original plan.