Question

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.

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
)





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Answer 1

Let's analyze the situation considering the information given.

### Part A:

1. **Slope (m):**
Since Penny spends $12 each week, the slope, which represents the rate of change of money left per week, is -12. This is negative because she is spending money.

\( m = -12 \)

2. **Point that we know:**
After 4 weeks, Penny has $134 left. This gives us a point:

\( (x, y) = (4, 134) \)

### Part B:

To write the linear equation in slope-intercept form \(y = mx + b\):

- We already have the slope \(m = -12\).
- To find the y-intercept \(b\), we can use the point \((4, 134)\).

Using the slope-intercept form, we can plug in the point:

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

Now calculate:

\[
134 = -48 + b
\]

To find \(b\), add 48 to both sides:

\[
b = 134 + 48
\]
\[
b = 182
\]

Now we can write the final equation:

\[
y = -12x + 182
\]

### Final Answers:

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

- **Part B:**
- \( y = -12x + 182 \)