Write a linear eq. expressing S as a function of L for the problem below?

Question

If a child's foot is 7.75", then the child wears a size 13. If the child foot is 5.75 the child wears size 7. The shoe size S is a linear function of the length of the foot L.

Answer 1

A linear eq has the form y = ax + b; for this problem, S = aL + b, and you need to find values for a and b (two unknowns). You are given two conditions: S = 13 when L = 7.75, and S = 7 when L = 5.75. Set up the equations:

13 = a*7.75 + b
7 = a*5.75 + b

Solve for a and b by any of the methods used for simultaneous linear equations.

Ex: subtract the second eq from the first to get

6 = 2*a. or a = 3

Then put a into either equation to get b:

13 = 7.75*3 + b, or b = 13 - 3*7.76 = -10.25

so the linear eq is

S = 3*L - 10.25