Answer:
[tex]m=7w+4[/tex]
Step-by-step 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
[tex]\displaystyle m-m_1=\frac{m_2-m_1}{w_2-w_1}(w-w_1)[/tex]
Let's plug in our values
[tex]\displaystyle m-11=\frac{25-11}{3-1}(w-1)[/tex]
Simplifying:
[tex]m-11=7w-7[/tex]
[tex]\boxed{m=7w+4}[/tex]
