Question

Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is 2/5?

Answer 1

Parallel: line p with slope 2/5
Perpendicular: line n with slope -5/2
the other two would be neither.

Answer 2

Answer:The line p is parallel , n is perpendicular, line m and q are neither parallel not perpendicular.

Step-by-step explanation:

The slope of given line is
`(2)/(5)`.

The slope of parallel line are equal.

Only the slope of line p is
`(2)/(5)` which is equal to the slope of given line, therefore the line p is parallel to the given line.

The product of slopes of perpendicular lines is -1.

The slope of n is
`(-5)/(2)` and the slope of given line is
`(2)/(5)`.

`(2)/(5)* (-5)/(2) =-1`

Since the product of slopes is -1, so the line n is perpendicular to the given line.

The slope of m is
`(5)/(2)` and the slope of given line is
`(2)/(5)`.

`(2)/(5)* (5)/(2) =1`

Since the product of slopes is not equal to -1, so the line m is not perpendicular to the given line.

The slope of q is
`(-2)/(5)` and the slope of given line is
`(2)/(5)`.

`(2)/(5)* (-2)/(5) =-(4)/(25)`

Since the product of slopes is not equal to -1, so the line q is not perpendicular to the given line.

Therefore the line m and q are neither parallel not perpendicular.