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.

Question

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

To solve this problem, let's break it down into the parts you mentioned.

Part A: Identify the slope and a point.

Penny is spending $12 each week on treats for her pets, which represents the slope \( m \) in our linear equation. Since she is spending, the slope is negative:

\[ m = -12 \]

Now, we also know that after 4 weeks, she has $134 left. This gives us a point (x, y) where x is the number of weeks and y is the total money left:

• After 4 weeks, \( x = 4 \) and \( y = 134 \).

So, the point we know is:

\[ (4, 134) \]

Part B: Write the linear equation.

To write the linear equation in slope-intercept form \( y = mx + b \), we can use the slope and the point we have:

1. We already found the slope \( m = -12 \).
2. We need to find the y-intercept \( b \). We can use the point (4, 134) to find \( b \):

Using the slope-intercept formula: \[ y = mx + b \]

Substituting the values of \( y \), \( m \), and \( x \): \[ 134 = -12(4) + b \]

Calculating the right side: \[ 134 = -48 + b \]

Solving for \( b \): \[ b = 134 + 48 = 182 \]

Now we have our slope \( m \) and y-intercept \( b \). Thus, the linear equation is:

\[ y = -12x + 182 \]

Final Answers:

Part A:

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

Part B:

• The linear equation that models the total money left is \( y = -12x + 182 \)