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How to Know If Two Equations Are Perpendicular

Two lines are said to be perpendicular if their intersection creates 90-degree angles. Each corner of a square is formed where two perpendicular lines meet. The 90-degree angle of a right triangle is also formed by two perpendicular lines. Two lines will always have an intersection point, unless they are parallel to each other. The equations of lines can be analyzed to determine if the are parallel or perpendicular. If the slope of one line is the negative reciprocal of the slope of the other line, the two lines are perpendicular.

Instructions

- 1
  Format each of the equations to the form y = mx + b. In this equation, x and y are the variables that represent points on the Cartesian coordinate plane, m is the slope of the line and b is a constant that represents the y-intercept of the line. For example, if y - 3x = 12 is given as an equation, format it to y = 3x + 12.
- 2
  Find the reciprocal of the slope, or m value, of the first line. For example, if the equation is y = 3x + 12, the reciprocal of m is 1/3.
- 3
  Convert the number from the previous step to negative. In this example, the process yields -1/3.
- 4
  Compare the slope of the other equation to see if it matches the value from the previous step. If it does, then the lines are perpendicular to each other.

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