SOLUTION: Hello, How do you find where a liine intercepts another point on a graph. For example: Line y=2/3x+13.5 and Line y=-1/2x+3 where do they intersect? thank you

Algebra ->  Graphs -> SOLUTION: Hello, How do you find where a liine intercepts another point on a graph. For example: Line y=2/3x+13.5 and Line y=-1/2x+3 where do they intersect? thank you      Log On


   

Question 7181: Hello,
How do you find where a liine intercepts another point on a graph.
For example:
Line y=2/3x+13.5 and Line y=-1/2x+3
where do they intersect?
thank you
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
they intersect...think about it...this is where the 2 lines are equal. So at that point, their x-vlaues are the same and their y-values are the same.

So, we have y=2/3x+13.5 and y=-1/2x+3, so we can equate their y-values, as follows:

2/3x+13.5 = -1/2x+3 --> assuming it is just 1/2x and not 1/(2x+3)...you really show use brackets more, to avoid confusion!

%282%2F3x%29%2B13.5+=+-%281%2F2x%29%2B3
%282%2F3x%29%2B%281%2F2x%29+=+3-13.5
%284%2F6x%29%2B%283%2F6x%29+=+-10.5
7%2F6x+=+-10.5 --> moving the x to the righthand side and the -10.5 to the lefthand side gives
-7%2F6%2810.5%29+=+x
-7/63 = x

--> x = -1/9

jon.