Suppose you have 2 lines: l and k. If l and k are perpendicular to each other, then the slope of perpendicular line k is the negative reciprocal of the slope of line l, ie Slopek = -1/Slopel
The following shows you how to determine the slope of a line and the slope of its perpendicular line:
- Determine the slope of the first line by looking at the equation. A standard line equation is written as y = mx+b where the letter "m" is the slope, and "b" is the value where the lines will cross the y-axis. If the equation is y = 5x-3, then the slope of the line is 5.
- Find the negative reciprocal of the slope of the first line by flipping the fraction and using the opposite sign. If the original slope is 5, the negative reciprocal is -1/5. This is the slope of the second line, the one perpendicular to the line in the equation.
- A line can have many lines perpendicular to it. So to graph a perpendicular line, we will need a point that it crosses. Suppose the perpendicular line crosses point (0, -3), ie, it crosses the y-axis at the same position as the 1st line. Then the equation of this perpendicular line will be y = -1/5x-3.