Determine whether the two given lines are parallel, perpendicular, or neither.
-
A) parallel
B) perpendicular
C) neither

Question

Determine whether the two given lines are parallel, perpendicular, or neither.
-
A) parallel 
B) perpendicular 
C) neither

Quizplus · Accepted Answer

To determine whether the two lines are parallel or perpendicular, we need to look at their slopes. 
The slope of the line 11ebb63d_1b47_2668_b851_ff7d2f7c3db6_TB8475_11 can be found by rearranging the equation in slope-intercept form, y = mx + b, where m is the slope:
6x + 2y = 10
2y = -6x + 10
y = -3x + 5
So the slope of the first line is -3.

The slope of the line TB8475_11 can be found similarly:
2x + 6y = 8
6y = -2x + 8
y = (-1/3)x + 4/3
So the slope of the second line is -1/3.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if m1 * m2 = -1.

(-3) * (-1/3) = 1
Since the product is not -1, the two lines are not perpendicular.

Two lines are parallel if and only if their slopes are equal. That is, if m1 = m2.

Since -3 and -1/3 are not equal, the two lines are not parallel either. Therefore, the answer is C) neither. Two lines are perpendicular if and only if the product of their slopes is - 1. Therefore the line is perpendicular.

Determine Whether the Two Given Lines Are Parallel, Perpendicular, or Neither