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 [tex]\frac{2}{5}[/tex].
The slope of parallel line are equal.
Only the slope of line p is [tex]\frac{2}{5}[/tex] 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 [tex]\frac{-5}{2}[/tex] and the slope of given line is [tex]\frac{2}{5}[/tex].
[tex]\frac{2}{5}\times \frac{-5}{2} =-1[/tex]
Since the product of slopes is -1, so the line n is perpendicular to the given line.
The slope of m is [tex]\frac{5}{2}[/tex] and the slope of given line is [tex]\frac{2}{5}[/tex].
[tex]\frac{2}{5}\times \frac{5}{2} =1[/tex]
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 [tex]\frac{-2}{5}[/tex] and the slope of given line is [tex]\frac{2}{5}[/tex].
[tex]\frac{2}{5}\times \frac{-2}{5} =-\frac{4}{25}[/tex]
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.
