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
)

Answer 1

Sure! Let’s work through the problems step by step.

### Problem 1:
Tommy the cat's hair tie stealing habits.

#### Part A
Tommy starts with 5 hair ties and steals 3 more each day. We can express the total number of hair ties \( h \) as a function of the number of days \( d \):

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

#### Part B
To find out how many hair ties Tommy has stolen after 9 days, substitute \( d = 9 \) into the equation:

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

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

---

### Problem 2:
Penny's monetary reward for returning a puppy.

#### Part A
Penny spends $12 each week. Thus, the slope \( m \) of her spending is \(-12\) (since it's a decrease).

We know that after 4 weeks, she has $134 left. We can represent this point as:

\[
\text{Point: } (4, 134)
\]

So, the values are:
- \( m = -12 \)
- A point that we know is \( (4, 134) \)

#### Part B
To write a linear equation that models the total money left \( y \) after \( x \) weeks, we can use the point-slope form and convert it to slope-intercept form. The general form of the line is:

\[
y = mx + b
\]

Using the slope \( m = -12 \) and the point \( (4, 134) \):

First, calculate \( b \) using the point:

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

Now we have \( m \) and \( b \):

\[
y = -12x + 182
\]

So the equation that models the total money left after \( x \) weeks is:

\[
y = -12x + 182
\]