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

Let's analyze the situation considering the information given.

Part A:

1. Slope (m):
   Since Penny spends $12 each week, the slope, which represents the rate of change of money left per week, is -12. This is negative because she is spending money.

   \( m = -12 \)

2. Point that we know:
   After 4 weeks, Penny has $134 left. This gives us a point:

   \( (x, y) = (4, 134) \)

Part B:

To write the linear equation in slope-intercept form \(y = mx + b\):

• We already have the slope \(m = -12\).
• To find the y-intercept \(b\), we can use the point \((4, 134)\).

Using the slope-intercept form, we can plug in the point:

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

Now calculate:

\[ 134 = -48 + b \]

To find \(b\), add 48 to both sides:

\[ b = 134 + 48 \] \[ b = 182 \]

Now we can write the final equation:

\[ y = -12x + 182 \]

Final Answers:

• Part A:

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

• Part B:

  • \( y = -12x + 182 \)