Question

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
What is the slope and what is one point that we know
m = ___
A point that we know is _____ (ordered pair)
Write a linear equation that model the total money left ,y, from her reward after x weeks
y + ____ ( y=mx+b form)

Answer 1

To find the slope and the equation that models the total money left, we can start by analyzing the information given.

1. **Determine the initial amount earned (b)**:
- After 4 weeks, Penny has $134 left.
- She spends $12 each week. Therefore, after 4 weeks, she has spent: \( 12 \times 4 = 48 \) dollars.
- Let \( x \) be the total monetary reward she initially earned. Then we can set up the equation:
\[
x - 48 = 134
\]
- Solving for \( x \):
\[
x = 134 + 48 = 182
\]
- So, the initial amount she earned was $182.

2. **Calculate the slope (m)**:
- The spending rate is $12 per week, which means her money decreases by $12 for each week that passes. Therefore, the slope \( m \) is:
\[
m = -12
\]

3. **Identify a point**:
- After 4 weeks, she has $134 left. This gives us the point:
\[
(x, y) = (4, 134)
\]

4. **Write the linear equation**:
- The general form of a linear equation is \( y = mx + b \).
- We already have \( m = -12 \) and \( b \) is the initial amount, which is $182.
- Thus, the equation is:
\[
y = -12x + 182
\]

5. **Fill in the blank**:
- The slope: \( m = -12 \)
- A point that we know: \( (4, 134) \)
- The linear equation that models the total money left \( y \):
\[
y = -12x + 182
\]

So to summarize:
- \( m = -12 \)
- A point that we know is \( (4, 134) \)
- The equation is \( y = -12x + 182 \)