During each week of piano lessons, William learns to play 2 new pieces. Write an equation that shows the relationship between the weeks of lessons x and the total number of pieces learned y.

We are tasked with finding the equation that represents this relationship (the number of weeks that William has received piano lessons and the total number of piano pieces that William has learned).

The number of weeks that William has attended piano lessons is represented by the variable x.
The total number of piano pieces that William has learned is represented by the variable y.

Therefore, take for example that William has been taking piano lessons for four months. This would roughly equate to sixteen weeks.

[tex]x=16[/tex]

After analyzing this, we know that he learns two pieces a week. So, we can multiply our number of weeks by two in order to receive the total amount of pieces learned.

[tex]x \times 2[/tex]

Finally, we need to set this equal to the total number of pieces learned, or our previously defined variable y.

[tex]y=x\times 2[/tex]

In mathematics, we want to simplify everything as much as possible. There is a statement that if a constant and a variable are to be multiplied, we can remove the multiplication symbol and place the constant and the variable together.

[tex]y=2x[/tex]

Therefore, our equation is [tex]\bold{y = 2x}[/tex].