Question

Suppose we are given the following.

Line 1 passes through (0, 4) and (-3, 8).
Line 2 passes through (-4,-2) and (4, 4).
Line 3 passes through (4, 1) and (8, 4).
(a) Find the slope of each line.
Slope of Line 1 = 0
0
Slope of Line 2 =
Slope of Line 3 =
0
►
(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.

Answer 1

1. slope: -4/3, perpendicular to lines 2 and 3
2. slope: 3/4, parallel to line 3, perpendicular to line 1
3. slope: 3/4, parallel to line 2, perpendicular to line 1

Explanation:

Given pairs of points that define three lines, you want to know their slopes, and whether line pairs are parallel or perpendicular.

The lines are defined by point pairs ...

1. (0, 4) and (-3, 8)
2. (-4, -2) and (4, 4)
3. (4, 1) and (8, 4)

Slope

The slope of a line is given from a pair of points by the formula ...

m = (y2 -y1)/(x2 -x1)

Lines with the same slope are parallel.

Lines with opposite reciprocal slope are perpendicular.

Application

Line 1 slope = (8 -4)/(-3 -0) = 4/-3 = -4/3

Line 2 slope = (4 -(-2))/(4 -(-4)) = 6/8 = 3/4

Line 3 slope = (4 -1)/(8 -4) = 3/4

The slopes of the lines are ...

1. -4/3
2. 3/4
3. 3/4

Relation of line pairs

Lines 1 and 2 have slopes that are opposite reciprocals (-4/3 and 3/4), so are perpendicular.

Lines 1 and 3 have slopes that are opposite reciprocals (-4/3 and 3/4), so are perpendicular.

Lines 2 and 3 have identical slopes (3/4 and 3/4), so are parallel.