How to Give the Slope of a Line Perpendicular to the Line

Perpendicular lines intersect at right angles.

In basic algebra, two lines are said to be perpendicular if they intersect each other at right angles. Calculate the slope of a line perpendicular to another line by determining the slope of the original line and finding the opposite reciprocal. This gives you the slope of the line that is perpendicular to the first line.

Instructions

1. Identify the coordinate values x and y of two separate points on the line. The x value of a point on the line is its distance from the y-axis; the y value of a point is its distance from the x-axis.

2. Use the slope formula to find the slope of the line. The slope of a line is labeled m and is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two separate points on the line. For example, if the two points you identified in Step 1 were (3, 3) and (2, 6), you would calculate (6 - 3) / (2 - 3) to get the value m = -3.

3. Calculate the slope of a line perpendicular to the line by taking the opposite reciprocal of m, or -1/m. The opposite of a number is its negative value if it is positive and its positive value if it's negative. The reciprocal of a number is the number with its numerator and denominator reversed. In the example, the reciprocal of -3 is 1/3.

References

• Purplemath: Parallel and Perpendicular Lines