Question

Tatiana works as a landscaper trimming bushes and shrubs. She can trim 5 bushes per hour. At a large office building, she has already trimmed 15 bushes.

Plot the function that shows the number of hours, h, it will take for Tatiana to trim b additional bushes.

Answer 1

To represent the relationship between the number of additional bushes \( b \) that Tatiana can trim and the number of hours \( h \) it will take her, we can use the formula based on her trimming rate.

Tatiana trims bushes at a rate of 5 bushes per hour, so for every hour of work, she trims 5 bushes. The function that relates the number of bushes trimmed to time can be expressed as:

\[
h = \frac{b}{5}
\]

Where:
- \( h \) is the number of hours it takes to trim \( b \) additional bushes.
- \( b \) is the number of additional bushes.

### Steps to Plot the Function

1. **Choose Values for \( b \)**: You can choose a range of values for \( b \) (e.g., 0, 5, 10, 15, 20, 25, 30).
2. **Calculate Corresponding Values for \( h \)**: For each value of \( b \), calculate \( h \) using the formula \( h = \frac{b}{5} \).

### Sample Calculation
Here's how the calculations would look for selected values of \( b \):

- If \( b = 0 \):
\[
h = \frac{0}{5} = 0 \, \text{hours}
\]

- If \( b = 5 \):
\[
h = \frac{5}{5} = 1 \, \text{hour}
\]

- If \( b = 10 \):
\[
h = \frac{10}{5} = 2 \, \text{hours}
\]

- If \( b = 15 \):
\[
h = \frac{15}{5} = 3 \, \text{hours}
\]

- If \( b = 20 \):
\[
h = \frac{20}{5} = 4 \, \text{hours}
\]

- If \( b = 25 \):
\[
h = \frac{25}{5} = 5 \, \text{hours}
\]

- If \( b = 30 \):
\[
h = \frac{30}{5} = 6 \, \text{hours}
\]

### Data Points
From the calculations, we have the following data points:
- \( (0, 0) \)
- \( (5, 1) \)
- \( (10, 2) \)
- \( (15, 3) \)
- \( (20, 4) \)
- \( (25, 5) \)
- \( (30, 6) \)

### Plotting
Using these data points, you can plot a graph where the x-axis represents the number of additional bushes \( b \) and the y-axis represents the time in hours \( h \).

The resulting graph will be a straight line passing through the origin (0,0) with a slope of \( \frac{1}{5} \) because for every increase of 5 bushes, the time increases by 1 hour.

### Conclusion
The function \( h = \frac{b}{5} \) accurately models the relationship between the number of additional bushes trimmed and the time taken for that task. This is a simple linear function that is easy to interpret and visualize.