Question

What is the slope of the line perpendicular to `y=12/11x-9`?

Answer 1

The slope of the line perpendicular to `y = 12/11x - 9` is `-11/12`.

Explanation:

Perpendicular lines are lines which intersect at a 90 degree angle.

For example, `y = 2/5x + 1` has a slope of `2/5`, and the line `y = -5/2x + 2` has a slope of `-5/2`.

Do you notice anything about these two slopes? We find that the two fractions are "flipped", and one is positive while the other is negative. These are opposite reciprocals.

The positive/negative slopes are the opposite parts, and the "flipping" is the reciprocal part. The slopes of two perpendicular lines should always have a product of `-1`.

For instance, in the example above, `2/5 * -5/2 = -1`, so these are perpendicular lines.

The easiest way to tell if two lines are perpendicular is to find their slopes and compare them. If they are opposite reciprocals, then the lines are perpendicular.

On a side note, two lines are parallel if their slopes are the same, or equal (such as `y = 1/2x = 4` and `y = 1/2x - 7`).