Worksheet page with two word problems requiring interpretation of slope and y-intercept in real-world scenarios.

Problem 1: Jude's Car Loan

The equation given is:
\[ r = 7245 - 201.25m \]
where:
- \( r \) is the amount remaining on the loan.
- \( m \) is the number of months of payment.

#### Step 1: Identify the slope and y-intercept
The equation is in the slope-intercept form:
\[ y = mx + b \]
where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

For the equation \( r = 7245 - 201.25m \):
- The slope (\( -201.25 \)) is the coefficient of \( m \).
- The y-intercept (\( 7245 \)) is the constant term.

So, the slope is \( -201.25 \) and the y-intercept is \( 7245 \).

#### Step 2: Interpret the slope and y-intercept
- Slope (\( -201.25 \)): The negative slope indicates that the amount remaining on the loan decreases by $201.25 for each month of payment. This means Jude pays $201.25 per month toward his car loan.
- Y-intercept (\( 7245 \)): The y-intercept represents the initial amount of the loan when \( m = 0 \) (i.e., at the start of the loan). Therefore, the initial loan amount is $7245.

#### Final Answer for Problem 1:
\[
\boxed{\text{Slope: } -201.25, \text{ Y-intercept: } 7245}
\]

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Problem 2: Viola's Drum Practice

The equation given is:
\[ t = 60 - 3.5s \]
where:
- \( t \) is the number of minutes left in her practice session.
- \( s \) is the number of times she plays along with the new song.

#### Step 1: Identify the slope and y-intercept
The equation is in the slope-intercept form:
\[ y = mx + b \]
where:
- \( m \) is the slope.
- \( b \) is the y-intercept.

For the equation \( t = 60 - 3.5s \):
- The slope (\( -3.5 \)) is the coefficient of \( s \).
- The y-intercept (\( 60 \)) is the constant term.

So, the slope is \( -3.5 \) and the y-intercept is \( 60 \).

#### Step 2: Interpret the slope and y-intercept
- Slope (\( -3.5 \)): The negative slope indicates that the number of minutes left in her practice session decreases by 3.5 minutes for each time she plays along with the new song. This means Viola spends 3.5 minutes practicing each time she plays along with the song.
- Y-intercept (\( 60 \)): The y-intercept represents the total number of minutes in her practice session when \( s = 0 \) (i.e., before she starts playing along with the song). Therefore, the total duration of her practice session is 60 minutes.

#### Final Answer for Problem 2:
\[
\boxed{\text{Slope: } -3.5, \text{ Y-intercept: } 60}
\]

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Summary of Answers:

1. Jude's Car Loan:
- Slope: \( -201.25 \)
- Y-intercept: \( 7245 \)

2. Viola's Drum Practice:
- Slope: \( -3.5 \)
- Y-intercept: \( 60 \)

\[
\boxed{\text{Problem 1: Slope: } -201.25, \text{ Y-intercept: } 7245; \text{ Problem 2: Slope: } -3.5, \text{ Y-intercept: } 60}
\]