Let's solve
Problem 3 step by step.
---
Problem 3:
> In order to become a member of the library-all-you-can-read club, there is a
$40 sign-up fee and a
$2 monthly fee. Write an equation in
slope-intercept form that models this situation.
---
Step 1: Understand the components
We are modeling a cost over time (monthly). The total cost depends on:
- A
one-time sign-up fee = $40 (this is a fixed cost, paid once)
- A
recurring monthly fee = $2 per month
Let:
- $ y $ = total cost (in dollars)
- $ x $ = number of months
---
Step 2: Use slope-intercept form
The
slope-intercept form of a linear equation is:
$$
y = mx + b
$$
Where:
- $ m $ = slope (rate of change) → monthly fee
- $ b $ = y-intercept (initial value) → sign-up fee
So:
- $ m = 2 $ (since $2 per month)
- $ b = 40 $ (the one-time sign-up fee)
---
Step 3: Plug into the equation
$$
y = 2x + 40
$$
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✔ Final Answer:
$$
\boxed{y = 2x + 40}
$$
This equation models the total cost $ y $ after $ x $ months of membership.
---
🔍 Explanation:
- After 0 months: $ y = 2(0) + 40 = 40 $ → just the sign-up fee
- After 1 month: $ y = 2(1) + 40 = 42 $
- After 2 months: $ y = 2(2) + 40 = 44 $
- And so on...
Each month adds $2 to the total cost, starting from $40.
Let me know if you'd like help with any other problems!
Parent Tip: Review the logic above to help your child master the concept of slope intercept form word problems worksheet.
