Question

Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is −34?

Parallel Perpendicular Neither

Line M, with slope3/4 Line N, with slope 4/3 Line P, with slope -4/3 Line Q, with slope -3/4

Answer 1

Given:

The slope of a line is
`-(3)/(4)`.

To find:

The lines in the options are parallel, perpendicular or neither parallel nor perpendicular to the given line.

Solution:

We know that the slopes of parallel lines are equal.

The slope of line Q and the slope of given line are same, i.e.,
`-(3)/(4)`. So, the line Q is parallel to the given line.

The slope of a perpendicular line is the opposite reciprocal of the slope of the line because the product of slopes of two perpendicular lines is -1.

The slope of a line is
`-(3)/(4)`. It means the slope of the perpendicular line must be
`(4)/(3)`. So, the line N is perpendicular to the given line.

The slopes of line M and P are neither equal to the slope of the given line nor opposite reciprocal of the slope of the line.

Therefore, the lines M and P are neither parallel nor perpendicular.