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.

Question

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.

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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:

\[ y = -12x + 182 \]