# a coordinate geometry help

• Sep 22nd 2008, 12:57 PM
mitchoboy
a coordinate geometry help
hey im stuck on this one question. its maths c1. Its got to be in 2moz.

1. The 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

thanks.

• Sep 22nd 2008, 01:08 PM
icemanfan
The slope of AP is $\displaystyle \frac{y - 0}{x - 3}$

and the slope of BP is $\displaystyle \frac{y - 6}{x - 5}$.

Since both AP and BP are segments of the same line, their slopes are equal. Equating the two expressions for the slope should give you the equation of the line.
• Sep 22nd 2008, 01:12 PM
mitchoboy
Quote:

Originally Posted by icemanfan
The slope of AP is $\displaystyle \frac{y - 0}{x - 3}$

and the slope of BP is $\displaystyle \frac{y - 6}{x - 5}$.

Since both AP and BP are segments of the same line, their slopes are equal. Equating the two expressions for the slope should give you the equation of the line.

hey thanks for the answer but how do you get $\displaystyle \frac{y - 0}{x - 3}$ and $\displaystyle \frac{y - 6}{x - 5}$.
• Sep 22nd 2008, 01:19 PM
icemanfan
The formula to calculate slope between two points $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ is $\displaystyle \frac{y_2 - y_1}{x_2 - x_1}$. All I did was to substitute the values for that formula from (3, 0) and (x, y) for the first slope and from (5, 6) and (x, y) for the second slope.
• Sep 22nd 2008, 01:31 PM
mitchoboy
thanks so much i get it now lol