Find two points on one of the lines. Points on a line are labeled with coordinates. The first coordinate indicates the point's position in relation to the x axis, and the second coordinate in a set indicates the point's position in relation to the y axis. Consider the example a line that possesses the points (1, 2) and (2, 4). The first set of coordinates can be represented by (x1, y1) and the second set can be represented by (x2, y2).
Subtract y2 from y1. In this example, you would subtract 4 from 2 to get -2. Then subtract x2 from x1. In this instance, you would subtract 2 from 1 to get -1.
Place the answers from step two in a fraction. Write the answer to y2 - y1 as the numerator (on top) and the answer to x2 - x1 as the denominator (on bottom). In this example, you would write -2/-1, which simplifies to 2/1 or 2. This is the slope the first line.
Repeat this process to find the slope of any line intersecting the first line. If the slope of any other line is the negative reciprocal of the first line's slope, then the lines are perpendicular. A negative reciprocal means that you write first line's slope as a fraction, reverse the numerator and denominator and change the sign of the fraction. In this case, you would flip 2/1 to 1/2 and add a negative, making it -1/2. Therefore, in this example, a line having a slope of -1/2 would be perpendicular to a line with a slope of 2/1.