Question

Membership for a robotics club is $15 per month plus a one-time registration fee of $35. Write an equation in slope-intercept form to represent the total cost y after any number of months x.

Answer 1

To represent the total cost \( y \) after any number of months \( x \), you can set up the equation based on the given membership fee structure:

1. The one-time registration fee is $35.
2. The membership fee is $15 per month.

The total cost \( y \) can be expressed as the sum of the registration fee and the monthly fees. The monthly cost depends on the number of months \( x \).

The equation will have the form:
\[ y = mx + b \]

where:
- \( m \) is the slope (the cost per month),
- \( b \) is the y-intercept (the initial cost, or the registration fee).

In this case:
- \( m = 15 \) (the monthly fee),
- \( b = 35 \) (the registration fee).

Putting it all together, the equation becomes:
\[
y = 15x + 35
\]

This equation represents the total cost \( y \) after any number of months \( x \).