Easy Algebra Step-by-Step

178 Easy Algebra Step-by-Step

Finding the Slope of a Line Through Two Points in the Plane

When you have two distinct points in a coordinate plane, you can construct

the line through the two points. The slope describes the steepness or slant (if

any) of the line. To calculate the slope of a line, use the following formula.

Slope of a Line Through Two Points

The slope m of a line through two distinct points,

(x 1 , y 1 ) and (x 2 , y 2 ), is given by

Slope =m=yy

xx

21 y

21 x

, provided x 1 ≠x 2

From the formula, you can see that the slope

is the ratio of the change in vertical coordinates

(t he rise) to the change in horizontal coordinates (the

run). Thus, slope =

rise

run

. Figure 16.4 illustrates the

rise and run for the slope of the line through points P 1 (x 1 , y 1 ) and P 2 (x 2 , y 2 ).

y

x

P 1

P 2

Rise y 2 – y 1

Run

x 2 – x 1

Figure 16.4 Rise and run

You w i l l fi nd it helpful to know that lines that slant upward from left to

right have positive slopes, and lines that slant downward from left to right

have negative slopes. Also, horizontal lines have zero slope, but the slope for

vertical lines is undefi ned.

P

When you use the slope

formula, be sure to subtract the

coordinates in the same order

in both the numerator and the

denominator. That is, if y 2 is

the fi rst term in the numerator,

then x 2 must be the fi rst term

in the denominator. It is also a

good idea to enclose substituted

negative values in parentheses to

guard against careless errors.