Problem Solving

In a rectangular co-ordinate system ,if a line pass through the points (-1o,-18 ) (20,22)and (x,2),what is the value of x ?

Given the points (-10, -18) and (20, 22), we can find the slope:

=(y2 - y1)/(x2 - x1)
=(22 - -18)/(20 - -10)
=40/30
=4/3

We can then use one of our existing points (I chose (20, 22) so I can stick with positive numbers) and the unknown point (x, 2) to solve:

4/3 = (y2 - y1)/(x2 - x1)
4/3 = (22 - 2)/(20 - x)
4/3 = 20/(20 - x) (cross multiply)
80 - 4x = 60 (subtract 80 from both sides)
-4x = -20

x=5

We could also have used the slope we found to count from one of our existing points. If we start with (20, 22), then we move 4 units down and 3 units to the left:

(20, 22)
(17, 18)
(14, 14)
(11, 10)
(8, 6)
(5, 2)