How to approach this coordinate system

[Chris8080]

Hi,

I've got a question like that:

In the coordinate system, if
(a, b) and (a+3, b+k)
are two points on the line find by the equation:
x = 3y - 7
than k = ?

When I see the solution, I almost understand it.
First I want to have y = mx + b which is y = (1/3)x + 7/3

After that it get's more difficult:
((b+k)-b) / (a + 3 - a) = k/3
Where do I know now, that I have to subtract the both points?

k/3 = 1/3
Is the subtraction of two points automatically the slope?

And the most important question for a suggestion:
I couldn't come up with an answer .. is there a website with a huge amount of questions like that or should I stick to the GMAT Review book and rely on my luck during the test?
I mean .. I couldn't solve this just because I didn't have an idea on how to approach and how to juggle the terms

Any suggestions for me?

Thank you in advance.
Bye, Chris

[scoobydooby]

if the 2 sets of points lie on the line, the co-ordinates of both the sets must satisfy the equation of the line.

putting (a, b) in the equation of the line (x=3y-7) we get
a=3b-7................1

putting (a+3, b+k) in the equation of the line (x=3y-7)
a+3=3(b+k)-7
=>a+3=3b+3k-7
=>a-3b=3k-7-3
=>-7=3k-10 (putting a-3b=-7 from .....1)
=>3=3k
=>k=1

[imhimanshu]

hi Chris,

Search for Coordinate Geometry and you may find tons of material on the net for the same. You may also get the problems on same.

Now, coming back your question where you found difficulty..
solution just applied the formulae (y2-y1)/(x2-x1) = m which is the slope formula..use it to find where coordinates are given and you need to find the slope. Also,since both points lie on single line...slope must be same.
thats why solution compared it with the slope you found from the equation y= mx+c
Hope its clear now.

[imhimanshu]

hi Chris,

Search for Coordinate Geometry and you may find tons of material on the net for the same. You may also get the problems on same.

Now, coming back your question where you found difficulty..
solution just applied the formulae (y2-y1)/(x2-x1) = m which is the slope formula..use it to find where coordinates are given and you need to find the slope. Also,since both points lie on single line...slope must be same.
thats why solution compared it with the slope you found from the equation y= mx+c
Hope its clear now.