‘The point P(x,y) lies on the straight line joining A(3,0) and B(5,6). Find the expressions for the gradients of AP and PB. Hence show that y=3x-9’
I understand the expressions for the gradients part; m(AP)= y – 0 / x – 3 = Y / x – 3.
M (PB)= y – 6 / x – 5
(Don’t know if this part helps): Length of AB= √(x₂-x₁)²+(y₂-y₁)² = √(5-3)²+(6-0)²= √4+36= √40
The part I don’t understand is ‘hence show that y=3x-9’. I know that m=3 and y intercept = -9, but how do you calculate/show this from the expressions of the gradient? Any help/ step-by-step will be appreciated.
I understand the expressions for the gradients part; m(AP)= y – 0 / x – 3 = Y / x – 3.
M (PB)= y – 6 / x – 5
(Don’t know if this part helps): Length of AB= √(x₂-x₁)²+(y₂-y₁)² = √(5-3)²+(6-0)²= √4+36= √40
The part I don’t understand is ‘hence show that y=3x-9’. I know that m=3 and y intercept = -9, but how do you calculate/show this from the expressions of the gradient? Any help/ step-by-step will be appreciated.