Justin is considering two websites for downloading music.The costs are detailed here.

Question

Website 1: a yearly fee of $30 and $1.50 for each download

Website 2: $2 for each download

What is a system of equations to represent the costs for one year?

Express your equations in the form of y=mx+b where x is the number of downloads for the year and y is the total cost for the year.

Enter your equations in the boxes.

Website 1:

Website 2: ​

Answer 1

To represent the costs for one year for each website as equations in the form of \( y = mx + b \), where \( x \) is the number of downloads, and \( y \) is the total cost, we can set up the following equations:

For Website 1:

• There is a yearly fee of $30 (which is the y-intercept, \( b \)), and each download costs $1.50 (which is the slope, \( m \)).
• Thus, the equation is:
  \[ y = 1.50x + 30 \]

For Website 2:

• There is no yearly fee (which means \( b = 0 \)), and each download costs $2 (which is the slope \( m \)).
• Thus, the equation is:
  \[ y = 2x + 0 \]
  (Note: This can alternatively be written simply as \( y = 2x \))

So, the final equations are:

• Website 1: \( y = 1.50x + 30 \)
• Website 2: \( y = 2x \)