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

If a child%26#039;s foot is 7.75%26quot;, 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.

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



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