I have this problem and I don't know how to work it out :

A graph is given with two lines and each have two points marked on them.

Line A - (1,4) and (2,8)
Line B - (5,2) and (5,6)

the question is:

If line A and line B were produced, they would meet at a point N. Determine the coordinates of N without drawing the graph.

I would appreciate if anyone helps me =)

Give this approach a whirl...

First, if you're given any two points on a line, that info is sufficient for deriving an equation for said line. So start with cooking up an equation for Line A, and one for Line B.

Next, if the two lines are not parallel, they WILL have a single intersection point. (At a glance, A and B are non-parallel, since B is vertical whereas A has a positive slope.) That single intersection point is a point (a,b) where a and b are the intersection's coordinates.

If (a,b) is the intersection point, then a and b satisfy both of the equations for the two lines.

So your two equations--one for Line A and one for Line B--represent two equations with two unknowns. Use either 'elimination' or 'substitution' to solve for x and y, and that unique solution represents the point (a,b) which is the intersection of the two lines.

think of it, find the algebraic value first
1,4 to 2.8 is slope of 4 y intercet of 0,0 so y=4x
5,2 to 5,6 is slope of infinite (vertcal) y intercept of 0,5 so x=5
so, now find y=4x with x=5 and there is the y value and 5 is the x value

y = mx + b

m = \frac{y_2 - y_1}{x_2 - x_1}

b = -mx_n + y_n

Figure the line equation (y=mx+b) for each of your given set of coordinates. Set them equal to each other.

Equation 1 = Equation 2

You should be able to get an X value, which if you plug into either equation, would give you the same result.

The x you find will be the x for that coordinate, and the y that you get from plugging it in will be the y for that coordinate.