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

x - 4y = -2
y = 8x - 9

1 answer

To determine whether the pair of lines is parallel, perpendicular, or neither, we need to examine the slopes of the lines.

The given equations are in the form of Ax + By = C, where A, B, and C are constants.

For the first equation x - 4y = -2, we can rearrange it to slope-intercept form y = mx + b by isolating y:

x - 4y = -2
-4y = -x - 2
y = (1/4)x + 1/2

From this equation, we can see that the slope of the first line is 1/4.

For the second equation y = 8x - 9, we can also see that the slope of the second line is 8.

Now, comparing the slopes of the two lines, we can see that the slopes are not equal (1/4 is not equal to 8). Therefore, the lines are not parallel.

Since the product of the slopes is not -1 (1/4 multiplied by 8 is not -1), the lines are also not perpendicular.

Therefore, the pair of lines x - 4y = -2 and y = 8x - 9 are neither parallel nor perpendicular.