Question

Rebecca must complete 15 hours
of volunteer work. She does
3 hours each day. Write a linear
equation in slope-intercept form
to represent the hours Rebecca still
has to work after x days.

Answer 1

To create a linear equation in slope-intercept form that represents the hours Rebecca still needs to work after \( x \) days, we can start by recognizing a few key points:

1. The total hours of volunteer work needed is 15 hours.
2. Rebecca does 3 hours of volunteer work each day.

Let \( y \) represent the hours of volunteer work Rebecca still has to complete after \( x \) days. After working for \( x \) days, she will have completed \( 3x \) hours.

The number of hours remaining can be expressed as:

\[
y = \text{Total Hours} - \text{Hours Worked}
\]
\[
y = 15 - 3x
\]

This is already in the linear equation form \( y = mx + b \), where:
- \( m \) (the slope) is \(-3\) (indicating that for each day worked, the hours remaining decrease by 3).
- \( b \) (the y-intercept) is \( 15\) (the starting total hours of volunteer work).

Thus, the linear equation in slope-intercept form that represents the hours Rebecca still has to work after \( x \) days is:

\[
y = -3x + 15
\]