F.3 maths

slope = difference between y-coordinate of the two points / difference between x-coordinate of the two points

a) (x , x^2) , (1 , x),where x is not =1

slope
= (x^2-x) / (x-1)
= [x(x-1)] / (x-1) where x is not =1 (所以分母同分子的(x-1) 可以約去）
= x


b) (a^2 + b^2 , a^2) , (2ab , b^2) , where a is not = b and a is not = -b

slope
= (a^2 - b^2) / [(a^2 + b^2) - 2ab)]
= [(a+b)(a-b)] / (a^2 - 2ab + b^2)
= [(a+b)(a-b)] / [(a -b)^2] where a is not = b (所以分母同分子的(a-b) 可以約去）
= (a+b) / (a-b)