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

Given:

The slope of a line is .

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., . 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 . It means the slope of the perpendicular line must be . 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.