What’s the relationship between perpendicular lines and slope?

The slope of two perpendicular lines must be in negative reciprocal relationship, if the slopes of two lines are negative reciprocals to each other, then these two lines must be perpendicular.

Example 1:

If line y=mx+2 and line y=4x+3 are perpendicular, what is the value of m?

Answer: Since the slope of two perpendicular lines must be in negative reciprocal relationship, m must be -1/4, which is the negative reciprocal of 4.

Note: Negative reciprocal means slope1 x slope2 = -1, in this case -1/4 * 4 = -1

Or you can set the unknown to be m, so: m * 4 = -1 and therefore m=-1/4

The slopes of any pair of perpendicular lines are in negative reciprocal relationship. The only exception is vertical line bing perpendicular to horizontal line, because vertical line has an undefined slope and horizontal line has a slope of 0,still vertical line must be perpendicular to horizontal line, y axis must be perpendicular to x axis.

Example 2:

Line 1 in point slope form is y=4x+10 and line 2 is y-9=-1/4(x-11). Are these two lines perpendicular?

Answer: Yes. Line one is in point slope form y=mx+b, slope m=4.

                       Line two is in the form (y-y1) =m(x-x1), slope m=-1/4

4 and -1/4 are negative reciprocals to each other, and therefore, these two lines are perpendicular.