Question

Tell whether the lines through the given points are parallel, perpendicular, or neither.

The slope of line 1 is (blank)

The slope of line 2 is (blank)

The two lines are (blank)



Please show all work on how you got your answer

Answer 1

Explanation:

The slope of a line connecting two points is:

m = (y₂ − y₁) / (x₂ − x₁)

The slope of line 1 is:

m = (4 − 0) / (7 − 1)

m = 2/3

The slope of line 2 is:

m = (6 − 0) / (3 − 7)

m = -3/2

Parallel lines have equal slopes.

Perpendicular lines have opposite inverse slopes.

2/3 and -3/2 are opposite inverses, so the lines are perpendicular.