What is the relationship between two lines and their coordinates?

[aek]

Hi all,
can some-one be kind enough to help me through this question. Thanks i highly appreciate it.

The line 2x+3y-8=0 cuts the x and y-axis at A and B respectively. The line y=ax+7 is called l. Find
(i) in terms of a, the coordinates of the point where l cuts AB

(ii)the value of a if l is to divide Ab internally in the ratio 1:3

 

[HallsofIvy]

Are you sure this isn't homework? Looks a lot like it!

On the x-axis, y= 0. If y= 0, then 2x- 8= 0. Solve for x to find A.
On the y-axis, x= 0. If x= 0, then 3y- 8= 0. Solve for y to find B.

The line y= ax+ 7 cuts the line 2x+ 3y-8= 0 at (x,y) that satisfies both equations simultaneously. Solve y= ax+ 7 and 2x+ 3y- 8= 0 for x and y (which will, of course, depend upon a).

If that point divides AB "in the ratio 1:3" then it must also divide the x (and y) values in that ratio. Determine a so that the difference between 0 and the x coordinate of the dividing point is 3 times the x-difference between A and the x coordinate of the dividing point.

 

[aek]

thanks for the hints HallsofIvy..yes it is homework, i just needed help to do it. Thanks again, i highly appreciate it.