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

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 \( y = -12x + 182 \)