Question

Determine the slope and y-intercept of the linear function represented by the following scenario:

Brooke's cell phone bill company charges her $15 for each additional gigabyte of data used plus a flat fee of $25.

Answer 1

To determine the slope and y-intercept of the linear function representing Brooke's cell phone bill, we can express the situation in a mathematical equation.

Let:
- \( x \) be the number of gigabytes of data used (beyond the flat fee).
- \( y \) be the total cost of the cell phone bill.

The function can be represented as:
\[
y = mx + b
\]

Where:
- \( m \) is the slope (the rate at which the cost changes with respect to the number of gigabytes).
- \( b \) is the y-intercept (the starting value of the cost when no additional gigabytes are used).

From the scenario:

1. **Slope (m)**: The cost for each additional gigabyte of data used is $15, which means the slope \( m = 15 \).

2. **Y-intercept (b)**: The flat fee before any additional usage is $25, which represents the starting value when no gigabytes are used, so \( b = 25 \).

Combining the information, we have:
- **Slope**: \( 15 \)
- **Y-intercept**: \( 25 \)

Therefore, the equation of the function can be written as:
\[
y = 15x + 25
\]

In summary:
- **Slope**: 15
- **Y-intercept**: 25