Easy Algebra Step-by-Step

The Cartesian Coordinate Plane 181

Step 3. State the slope.

The slope of the line that contains (5, 8) and (5, −3) is undefi ned.

Note: If you sketch the line through these two points, you will see

that it is a vertical line—so the slope should be undefi ned.

Slopes of Parallel and Perpendicular Lines

It is useful to know the following:

If two lines are parallel, their slopes are equal; if two lines are perpendicular,

their slopes are negative reciprocals of each other.

Problem Find the indicated slope.

a. Find the slope m 1 of a line that is parallel to the line through (−3, 4) and

(−1, −2).

b. Find the slope m 2 of a line that is perpendicular to the line through (−3, 4)

and (−1, −2).

Solution

a. Find the slope m 1 of a line that is parallel to the line through (−3, 4) and

(−1, −2).

Step 1. Determine a strategy.

Because two parallel lines have equal slopes, m 1 will equal the slope

m of the line through (−3, 4) and (−1, −2); that is, m 1 =m.

Step 2. Find m.

m=

yy

xx

y 1

21 x

=

()−

()− ()

)−^4

)−(−

=

−

−

24 −

13 +

=

− 6

2

= −3

Step 3. Determine m 1.

m 1 =m= −3

b. Find the slope m 2 of a line that is perpendicular to the line through (−3, 4)

and (−1, −2).

Step 1. Determine a strategy.

Because the slopes of two perpendicular lines are negative recipro-

cals of each other, m 2 will equal the negative reciprocal of the slope

m of the line through (−3, 4) and (−1, −2); that is, m

(^2) m

1

=−.

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