Please help with question Suppose that fx ax b is a linear

Please help with question

Suppose that f(x) = ax + b is a linear function. Use the definition of the average rate of change of a function to calculate the average rate of change of f between any two real numbers x_1 and x_2. Use your calculation in part (a) to show that the average rate of change of f is the same as the slope a.

Solution

f(x) = ax +b ;

a) { f(x2) -f(x1)/ ( x2 -x1) = { (ax2 +b) - (ax1 +b) }/( x2 -x1) = ( ax2 -ax1)/( x2 -x1)

b)   ( ax2 -ax1)/ ( x2 -x1) = a( x2 -x1)/( x2 -x1) = a { (x2 -x1) gets cancelled in num and denominator}