Intercept point?

Question

i have 2 straight lines

End coordinates for line 1:- (0,0) , (2,6.5)
End coordinates for line 2 :- (6.5,6.5) , (8.5,2)

at what point do these lines intercept?

Answer 1

As they are, they don't intercept. If you extend the lines so that they do, the extended interception point would be (3.8409,12.4830)

Answer 2

What you have to do, is solve a pair of simultaneous equations; where the simultaneous equations are the equations for the two lines, in the form y = gradient * x + offset.

Line 1: y = 3.25 * x
Line 2: y = -2.25 * x + 21.125

At the point where these lines meet, then x and y according to equation (1) will be equal to x and y according to equation (2). It is easiest to eliminate y;

3.25 * x = -2.25 * x + 21.125 ..... add 2.25 * x to both sides;
5.5 * x = 21.125 ..... divide both sides by 5.5;
x = 21.125 / 5.5

and then find y using one or other of the lines' equations:

y = 3.25 * 21.125 / 5.5

Since the point in question lies on both lines, it should satisfy the other equation: if it doesn't, then you mucked up somewhere. Finally, round your answer to a sensible precision.