Question

1. Tommy the cat is constantly stealing hair ties. At the start of the week, he had already stolen 5 hair ties. Each day, Tommy steals 3 more hair ties.

Part A: Write a linear equation that represents the total number of hair ties (h) based on the number of days that have passed (d).

h(d)=


Part B: Tommy would have stolen
hair ties after 9 days.



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

y=

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

Answer 2

part a of tommy the cat is wrong

Answer 3

Let's solve the problems step by step.

### Problem 1: Tommy the Cat

**Part A:** Start with the information given. At the start of the week (day 0), Tommy has stolen 5 hair ties, and he steals 3 more each day. We can write the linear equation:

- Initial amount of hair ties = 5
- Daily increase = 3 hair ties per day

The total number of hair ties after \(d\) days can be represented by:
\[
h(d) = 5 + 3d
\]

**Part B:** To find out how many hair ties Tommy has stolen after 9 days:

\[
h(9) = 5 + 3(9) = 5 + 27 = 32
\]

So, Tommy would have stolen **32 hair ties** after 9 days.

---

### Problem 2: Penny and the Reward

**Part A:** Penny spends $12 each week, and after 4 weeks she has $134 left.

1. The slope \(m\) of the linear function indicating how much money she has left can be described as the negative amount she spends per week. Therefore:

\[
m = -12
\]

2. One point we know is the amount she has after 4 weeks, which is given as (4, 134).

**Part B:** To write a linear equation that models the total money left \(y\) after \(x\) weeks, we start with the slope-intercept form \(y = mx + b\).

Given:
- Slope \(m = -12\)
- After 4 weeks, she has $134 left, so we need to find the y-intercept \(b\).

Using the point (4, 134):

\[
134 = -12(4) + b
\]
\[
134 = -48 + b
\]
\[
b = 134 + 48 = 182
\]

So, the equation becomes:

\[
y = -12x + 182
\]

### Final Answers

1. **Tommy the Cat:**
- Part A: \( h(d) = 5 + 3d \)
- Part B: **32** hair ties after 9 days.

2. **Penny and the Reward:**
- Part A:
- \( m = -12 \)
- A point that we know is \( (4, 134) \)
- Part B: \( y = -12x + 182 \)

Answer 4

For the linear equation in slope-intercept form (y = mx + b) that models Penny's total money left after x weeks, we already established:

1. The slope \( m \) is \(-12\), which represents the amount of money she spends each week.
2. The y-intercept \( b \) is \( 182\), which is the amount she started with before spending any money.

Thus, the complete equation is:

\[
y = -12x + 182
\]

This equation represents the total amount of money \( y \) that Penny has left after \( x \) weeks.

Answer 5

Let's reevaluate Part A of Tommy's problem.

Tommy initially had 5 hair ties at the start of the week (day 0), and he steals 3 more hair ties **each day**.

So the total number of hair ties he has stolen after \(d\) days would be:

1. **Initial amount of hair ties:** 5
2. **Hair ties stolen each day:** 3

The total number of hair ties after \(d\) days can be represented by the equation:

\[
h(d) = 3d + 5
\]

This means that after \(d\) days, Tommy has stolen a total of \(5\) hair ties plus \(3\) hair ties for each day that has passed.

### Summary of Correct Equation

- **Correct Linear Equation:**
\[
h(d) = 3d + 5
\]

If there's anything more specific you would like to address regarding this problem, please let me know!