Question

Marty is taking piano lessons. She is going to practice every afternoon. The 1st week she practiced for 11 minutes each day. The third week she practiced for 25 minutes each day. This is a linear relationship. Write an equation to represent that represents the number of minutes practiced daily, m, in relationship to the number of week, w.

Answer 1

`m=7w+4`

Explanation:

Linear Modeling

It consist is setting up a linear relationship between two variables, given some experimental data. Only 2 points are needed to set up the equation of a line, but if more than 2 points are used, then the result should use statistical approaches like linear regression to find the best-fit line.

For the question at hand, Marty practices his piano lessons 11 minutes the week #1. It provides the first point (1,11). He practices 25 minutes per day on the third week. It gives us another point (3,25). This is enough to find the equation of a line. The general formula for a line, having two points (m1,w1) (m2,w2) is

`\displaystyle m-m_1=(m_2-m_1)/(w_2-w_1)(w-w_1)`

Let's plug in our values

`\displaystyle m-11=(25-11)/(3-1)(w-1)`

Simplifying:

`m-11=7w-7`

`\boxed{m=7w+4}`