Coordinate Geometry Question?

hey guys. I have a question I'm stuck on.

The question is: Three points have coordinates A (2,9) B (4,3) C (2,-5). the line through C with gradient .5 meets the line AB produced at D. Calculate the coordinates of D.

I've started with drawing up a graph and plotting the points, however I do not know what to do afterwards to find the point of intersection D.

sorry for a pretty simple question, Maths isn't my strong point.

Would they be in form of y=mx+c?

I'm really not having a frickin clue as how to set this up for whatever reason.

So one of them is y= .5x + c
So I use the points of C for (X,Y)? So it becomes -5=.5(2) + C?

And the other line I found the gradient, so it's now y= -3x+C?
Again, do I use points from A & B or (X,Y)

So for the line passing through C, you have a line gradient 0.5, so it is of the form y=0.5x+c₁
To work out the c₁ you need to substitute the values of x and y for a point you know to be on the line, in this case, (2,-5); so you get $-5=0.5\cdot2+c_1 \Rightarrow c_1=-6$

If you then follow a similar procedure to get the line joining A and B, first having to find the gradient which, since it's a straight line, can be found by taking the difference in the y value of the two points and divide it by the difference in the x value. Then do exactly the same as above to find an equation for that line.

At this point you should have two equations of the form y=a₁x+c₁ and y=a₂x+c₂. You can then solve these simultaneous equations to find the x value of the intercept and then plug that into one of the two formulae that you found to get the y value.