Question

Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is 25? Drag each choice into the boxes to correctly complete the table. Parallel Perpendicular Neither line m, with slope 52line n, with slope −52line p, with slope 25line q, with slope −25

Answer 1

Parallel: line p, with slope 2/5

Perpendicular: line n, with slope -5/2

neither: line m, with slope 5/2 and line q, with slope -2/5

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Answer 2

We are given slope of a line as $\frac{2}{5}$.

We need to compare the slopes of other lines.

Note: When slopes are same lines are parallel.

When slopes are negative reciprocal the lines would be perpendicular.

When neither same nor negative reciprocal, lines neither parallel nor perpendicular.

1) Line n has slope : $\frac{5}{2}$.

5/2 is just reciprocal of 2/5.

Therefore, line n is neither parallel nor perpendicular.

2) Line p has slope : $\frac{-5}{2}$.

-5/2 is negative reciprocal of 2/5.

Therefore, line p is perpendicular to line m.

3) Line q has slope : $\frac{2}{5}$.

2/5 is equal to 2/5.

Therefore, line q parallel to line m.