Question 993320
{{{f(x) = mx + b}}}.


{{{f(x+k) = m(x+k) + b = mx + mk + b}}}.



{{{(f(x+k) - f(x)) / k = (mx + mk + b - (mx + b)) / k}}} which becomes:


{{{(f(x+k) - f(x)) / k = (mx + mk + b - mx - b) / k}}}.


when you combine like terms in the numerator, the mx and the -mx cancel out and the b and the -b cancel out and you are left with:


{{{(f(x+k) - f(x)) / k = (mk) / k}}}.


the k in the numerator and the denominator will cancel out and you will be left with:


{{{(f(x+k) - f(x)) / k = m}}}.