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.

Explanation:

The slope of given line is $\frac{2}{5}$.

The slope of parallel line are equal.

Only the slope of line p is $\frac{2}{5}$ 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 $\frac{-5}{2}$ and the slope of given line is $\frac{2}{5}$.

$\frac{2}{5}\times \frac{-5}{2} =-1$

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

The slope of m is $\frac{5}{2}$ and the slope of given line is $\frac{2}{5}$.

$\frac{2}{5}\times \frac{5}{2} =1$

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 $\frac{-2}{5}$ and the slope of given line is $\frac{2}{5}$.

$\frac{2}{5}\times \frac{-2}{5} =-\frac{4}{25}$

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.