Determine whether the pair of lines is parallel, perpendicular, or neither.

Question

x - 6y = - 6
y = 7x - 6

Choose the correct answer below.

OA. The two lines are neither parallel nor perpendicular.
OB. More information is needed.
O C. The two lines are parallel.
OD. The two lines are perpendicular.

Answer 1

To determine whether two lines are parallel or perpendicular, we need to compare their slopes.

The given equations are:
1) x - 6y = -6
2) y = 7x - 6

Rewrite equation 1 in slope-intercept form:
x - 6y = -6
-6y = -x - 6
y = (1/6)x + 1

Now we can compare the slopes:
- The slope of the first line is (1/6)
- The slope of the second line is 7

Since the slopes are not equal (1/6 ≠ 7), the two lines are not parallel.

To determine if the lines are perpendicular, we can check if the product of their slopes is -1. However, since the slopes are not equal, the lines cannot be perpendicular.

Therefore, the correct answer is:
OA. The two lines are neither parallel nor perpendicular.