Question

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

Line 1: (-7, -4), (5, 7)
Line 2: (2, 3), (14, 14)

a) Parallel
b) Perpendicular
c) Neither

Answer 1

The slopes of both Line 1 and Line 2 are 0.9167, which means they are parallel since their slopes are equal.

Step-by-step explanation:

To determine whether the given lines are parallel, perpendicular, or neither, we need to calculate the slopes of both lines and compare them. Two lines are parallel if their slopes are equal, and they are perpendicular if the product of their slopes is -1.

Calculation of Slopes:

For Line 1: Using the points (-7, -4) and (5, 7), the slope (m) is calculated as

m = (7 - (-4)) / (5 - (-7)) = 11 / 12 = 0.9167.

For Line 2: Using the points (2, 3) and (14, 14), the slope (m) is calculated as

m = (14 - 3) / (14 - 2) = 11 / 12 = 0.9167.

Since the slopes for Line 1 and Line 2 are equal, we can conclude that the lines are parallel.