Advertisement

So, in our last example...

In the point ( -2, -1 ), x1 = -2 and y1 = -1 ... and, in the point ( 4, 3 ), x2 = 3 and y2 = 3

m = ( y2 - y1 ) / ( x2 - x1 ) = ( 3 - ( -1 ) ) / ( 4 - ( -2 ) ) = 4 / 6 = 2 / 3

But, notice something cool...

The order of the points doesn't matter!  Let's switch them and see what we get:

In the point ( 4, 3 ), x1 = 4 and y1 = 3 ... and, in the point ( -2, -1 ), x2 = -2 and y2 = -1

m = ( y2 - y1 ) / ( x2 - x1 ) = ( -1 - 3 ) / ( -2 - 4 ) = -4 / -6 = 2 / 3 ... Same thing!

Let's try our new formula with the second example in the last lesson:

It was a line passing through

( -1, 4 ) and ( 2, -2 )

m = ( y2 - y1 ) / ( x2 - x1 ) = ( -2 - 4 ) / ( 2 - ( -1 ) ) = -6 / 3 = -2


YOUR TURN:

Without graphing, find the slope of the line that passes through the points

( 0, -3 ) and ( 5, 4 )