2. Penny earned a monetary reward for returning a lost puppy. She decides to spend $12 from the reward each week on treats for her own pets. After 4 weeks Penny has $134 left.

Question

Part A: What is the slope and what is one point that we know?

m=


a point that we know is
(write your response as an ordered pair)
Part B: Write a linear equation that models the total money left, y, from her reward after x weeks.

y=

(Write your answer in slope y-intercept form:y=mx+b
)

Answer 1

To solve the problem, we need to break it down into two parts as specified.

Part A:

1. Determine the slope (m): Since Penny spends $12 each week from the reward, the slope represents the rate at which her money decreases over time. Thus, the slope is:

   \[ m = -12 \]

   The negative sign indicates that the amount of money is decreasing over time.

2. Identify a point (x, y): After 4 weeks, Penny has $134 left. Therefore, the point we know is:

   \[ (4, 134) \]

Part B:

Now, we can write a linear equation that models the total money left, \(y\), from her reward after \(x\) weeks.

The equation in slope-intercept form is given by:

\[ y = mx + b \]

Where:

• \(m\) is the slope, which we determined to be -12.
• \(b\) is the y-intercept, representing the amount of money Penny had initially.

To find \(b\), we can use the point (4, 134):

\[ 134 = -12(4) + b \]

Calculating the right side:

\[ 134 = -48 + b \]

To isolate \(b\):

\[ b = 134 + 48 = 182 \]

Now, we can write the linear equation:

\[ y = -12x + 182 \]

Thus, the final answers are:

Part A:

• \(m = -12\)
• A point that we know is \((4, 134)\)

Part B:

• The linear equation is

\[ y = -12x + 182 \]