Finding the Slope of a Line, Given Two Points on it ?

Find the slope of the line passing through the pairs of points (-5, -2) and (2, 4).

One way to find the slope is to plot both points on the same grid. Then draw a right triangle, as shown below, and figure out the lengths of the two legs.

The slope of this line will be a positive number, since the line is going up from left to right.
The rise of the line is 6, since the vertical length is 6.
The run of the line is 7, since the horizontal length is 7.

The slope of a line is defined as "rise/run". So the slope of the line above is 6/7.
But another way to get the slope is by using the formula

Let (x1 , y1 ) = (-5, -2) and (x2 , y2 ) = (2, 4). Then m= 4-(-2)/2-(-5) = 4+2/2+5= 6/7

Now let's find the slope of the line passing through the following pairs of points:

(a) (0, 3) and (4, -1)
m= -1-3/4-0 = -4/4 = -1
(b) (-3, 3) and (6, 3)

m= 3-3/6-(-3) = 0+6+3 = 0/9 =0