What is the relationship between two lines and their coordinates?

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In summary, the problem involves finding the coordinates of the points where the lines 2x+3y-8=0 and y=ax+7 intersect. This can be solved by setting up equations and solving for x and y. To divide the line AB in the ratio 1:3, the x coordinate of the dividing point must be 3 times the difference between the x coordinate of A and the dividing point. The value of a can be determined using this information.
  • #1
aek
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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
 
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  • #2
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.
 
  • #3
thanks for the hints HallsofIvy..yes it is homework, i just needed help to do it. Thanks again, i highly appreciate it.
 

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