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Show y = 3x - 9

The point P(x,y) lies on the straight line joining A(3,0) and B(5,6). Find expressions for the gradients of AP and PB. Hence show that y = 3x - 9

I've calculated that the gradients are:

AP = y / 3-x

PB = 6-y / 5-x

How do i show that y = 3x-9? Totally lost...
Reply 1
Avatar for Hopple
Hopple
18
I think it wants you to set both gradients to be equal and rearrange to get y.
Reply 2
Avatar for mintmocha
mintmocha
13
They lie on a straight line, thus gradients should be the same as they'd be parallel.
Have you tried equating them?
If they all lie on the same line then the gradients are all the same.

Gradient of AP = y/(x-3) not y/(3-x)
The gradient of AB = 3.

so y/(x-3) = 3
(6-y)/(5-x)=3

Therefore

y(5-x)=(6-y)(x-3)

Expanding:
5y - yx= -18 - yx+3y + 6x
2y = 6x-18
y=3x-9
Original post by titsmcgee
If they all lie on the same line then the gradients are all the same.

Gradient of AP = y/(x-3) not y/(3-x)
The gradient of AB = 3.

so y/(x-3) = 3
(6-y)/(5-x)=3

Therefore

y(5-x)=(6-y)(x-3)

Expanding:
5y - yx= -18 - yx+3y + 6x
2y = 6x-18
y=3x-9


Thanks,

I've just started teaching myself C1-4.. and I keep making so many stupid little mistakes, like copying the question down wrong for forgetting to put -'s in nd stuff... :/ I'm sure this will stop with practise... haven't done maths in a few years

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