Because f is a linear function of x, the equation
f(x)=mx+b, where m and b are constants, can be used to define the relationship between x and
f(x). In this equation, m represents the increase in the value of
f(x) for every increase in the value of x by 1. From the table, it can be determined that the value of
f(x) increases by 8 for every increase in the value of x by 2. In other words, for the function
f the value of m is
, or 4.The value of b can be found by substituting the values of x and
f(x) from any row of the table and the value of m into the equation
f(x)=mx+b and solving for b. For example, using
x=1,f(x)=5, and
m=4 yields
5=4(1)+b. Solving for b yields
b=1. Therefore, the equation defining the function f can be writtenin the form
f(x)=4x+1.