Question
Determine the slope and y-intercept of the linear function represented by the following scenario:
Brooke and her friends decide to go bowling. The cost for the group is $15 for shoe rentals plus $4.00 per game.
Brooke and her friends decide to go bowling. The cost for the group is $15 for shoe rentals plus $4.00 per game.
Answers
GPT-4o mini
To determine the slope and y-intercept of the linear function representing the cost of bowling for Brooke and her friends, we can express the total cost mathematically.
Let's define:
- \( x \) as the number of games bowled.
- \( C \) as the total cost.
According to the problem, the cost consists of two components:
1. A fixed cost of $15 for shoe rentals.
2. A variable cost of $4.00 per game.
We can express the total cost \( C \) as follows:
\[
C = 15 + 4x
\]
In this linear equation \( C = 15 + 4x \):
- The term \( 15 \) represents the **y-intercept** (the cost when no games are played, or \( x = 0 \)). So, the y-intercept is \( (0, 15) \).
- The coefficient \( 4 \) in front of \( x \) represents the **slope**. This means that for each additional game played, the cost increases by $4.
To summarize:
- **Slope**: \( 4 \)
- **Y-intercept**: \( 15 \)
Thus, the slope is 4 and the y-intercept is 15.
Let's define:
- \( x \) as the number of games bowled.
- \( C \) as the total cost.
According to the problem, the cost consists of two components:
1. A fixed cost of $15 for shoe rentals.
2. A variable cost of $4.00 per game.
We can express the total cost \( C \) as follows:
\[
C = 15 + 4x
\]
In this linear equation \( C = 15 + 4x \):
- The term \( 15 \) represents the **y-intercept** (the cost when no games are played, or \( x = 0 \)). So, the y-intercept is \( (0, 15) \).
- The coefficient \( 4 \) in front of \( x \) represents the **slope**. This means that for each additional game played, the cost increases by $4.
To summarize:
- **Slope**: \( 4 \)
- **Y-intercept**: \( 15 \)
Thus, the slope is 4 and the y-intercept is 15.