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
)

Answer 1

To find the slope and a point that we know, we first need to understand Penny's spending pattern based on the provided information.

Part A:

1. Determine the slope (m): Penny spends $12 each week on treats, which means her remaining money decreases by $12 for each week that goes by. Therefore, the slope (m) is: \[ m = -12 \]

2. Identify a point that we know: After 4 weeks, Penny has $134 left. We can express this as the ordered pair \((4, 134)\).

So, summarizing Part A: \[ m = -12 \] \[ \text{a point that we know is } (4, 134) \]

Part B:

Next, we need to write a linear equation that models the total money left, \(y\), from her reward after \(x\) weeks.

Starting with the slope-intercept form \(y = mx + b\):

• From Part A, we know \(m = -12\).
• We also know that at \(x = 4\), \(y = 134\). We can use this point to find \(b\).

Now plug the point \((4, 134)\) into the equation:

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

Now we have both \(m\) and \(b\). Therefore, the linear equation that models the total money left is: \[ y = -12x + 182 \]

In summary for Part B: \[ y = -12x + 182 \]