1. Linear Functions(1 point)

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

1. Linear Functions

Part A

To write the linear equation for the total number of hair ties (h) based on the number of days (d) Tommy steals hair ties, we start with the initial number of hair ties he has stolen and add to it the number he steals each day. Tommy starts with 5 hair ties and steals 3 more each day.

The equation can be represented as:

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

Part B

To calculate the total number of hair ties Tommy would have stolen after 9 days, we substitute \( d = 9 \) into the equation.

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

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

---

2. Penny's Monetary Reward

Part A

Penny spends $12 each week on treats for her pets. The slope of her spending is \(-12\) because it represents the change in her money over time (money decreasing). We also know that after 4 weeks, she has $134 left.

So, the slope is:

\[ m = -12 \]

The point that we know after 4 weeks with $134 left is:

\[ (4, 134) \]

Part B

To write a linear equation that models the total money left \( y \) from her reward after \( x \) weeks, we can use the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Given that \( m = -12 \), we can calculate \( b \) using the point we know:

We know that \( y = 134 \) when \( x = 4 \).

Substituting these values into the equation:

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

\[ 134 = -48 + b \]

\[ b = 134 + 48 = 182 \]

Therefore, the linear equation in slope-intercept form is:

\[ y = -12x + 182 \]