# If the slope of a line is 1/3, what is the slope of a line perpendicular to this line?

Jun 26, 2018

The slope would be $- 3$. The rule is that the slope of a line perpendicular to a second line is the negative reciprocal of the second line's slope. The negative reciprocal of $x$, for instance, would be $- \frac{1}{x}$.

Jun 26, 2018

color(indigo)("Slope of perpendicular line " = -(1/m) = -(1 / (1/3)) = -3

#### Explanation:

$\text{Slope of the line } = m = \frac{1}{3}$

Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane).

On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees

$\text{Product of slopes of a pair of perpendicular lines } = - 1$

$\text{If " m " and " m' " are the slopes of the perpendicular lines, then}$

$m \cdot m ' = - 1$

color(indigo)("Slope of perpendicular line " = -(1/m) = -(1 / (1/3)) = -3