Perpendicular Lines and Slopes

Perpendicular lines are lines that intersect at right angles.

If you multiply the slopes of two perpendicular lines in the plane, you get –1. That is, the slopes of perpendicular lines are opposite reciprocals.

(Exception: Horizontal and vertical lines are perpendicular, though you can't multiply their slopes, since the slope of a vertical line is undefined.)

We can write the equation of a line perpendicular to a given line if we know a point on the line and the equation of the given line.

Example :

Write the equation of a line that passes through the point (1, 3) and is perpendicular to the line y = 3x + 2.

Perpendicular lines are lines that intersect at right angles.

The slope of the line with equation y = 3x + 2 is 3. If you multiply the slopes of two perpendicular lines, you get –1.

So, the line perpendicular to y = 3x + 2 has the slope .

Now use the slope-intercept form to find the equation.

We have to find the equation of the line which has the slope and passes through the point (1, 3). So, replace m with , x1 with 1, and y1 with 3.

Use the distributive property.

Add 3 to each side.

Therefore, the line is perpendicular to the line y = 3x + 2 and passes through the point (1, 3).