Algebra Know-It-ALL

Sometimes the slope of a straight line is informally called rise over run. This notion works
as long as the independent variable is on the horizontal axis, the dependent variable is on the
vertical axis, and we move to the right.

Try two points!

Suppose we see a line in the Cartesian plane, and are able to locate two points on it and deter-
mine their exact coordinates:

(x 1 ,y 1 )= (−2, 4)

and

(x 2 ,y 2 )= (3, 5)

The slope is ( y 2 − y 1 ), which we call Δy, divided by (x 2 − x 1 ), which we call Δx:

m=Δy/Δx

= (y 2 − y 1 )/(x 2 − x 1 )

= (5 − 4)/[3 − (−2)]

= 1 /(3+ 2)

= 1/5

This situation is illustrated in Fig. 15-1.

Slope-Intercept Form 237

–6 246

2

6

–2

–4

–6

x

y

–4 –2

(–2,4) (3,5)

m= y/ x

= (5 – 4) / [3 – (–2)]

= 1/5

Figure 15-1 The slope of a line can be calculated from

the coordinates of two points on that line.