Perpendicular Line Calculator

Two distinct lines in a coordinate plane are perpendicular if and only if the product of their slopes equals -1. This means that if you have a known slope represented as m1, the slope of any line perpendicular to it (m2) must be its negative reciprocal: m2 = -1 / m1. Once you establish the new slope m2 and pair it with a specific coordinate point (x, y) through which the line must pass, you can solve for the y-intercept (b) using the standard slope-intercept form equation: b = y - m2 * x. When evaluating intersections between two different linear functions, you can also determine the exact crossing point by setting their slope-intercept equations equal to one another.

Imagine you need to find the equation of a perpendicular line that passes through the specific coordinate point (4, 5), given an original line with a slope (m1) of 2. First, calculate the new perpendicular slope (m2) using the negative reciprocal formula: m2 = -1 / 2, which equals -0.5. Next, use the point-slope form or substitute the slope and your point (x = 4, y = 5) into the slope-intercept equation to find the y-intercept (b): b = 5 - (-0.5 * 4), which simplifies to b = 5 + 2 = 7. Therefore, the final equation of your perpendicular line is y = -0.5x + 7.

Always double-check your signs when converting a slope into its negative reciprocal; a common mistake is forgetting to flip the sign from positive to negative or vice versa. Remember that a horizontal line (slope of zero) has a perpendicular line that is vertical (undefined slope). When plotting your equations on a coordinate plane, ensure your graph axes share an equal scale so the 90-degree intersection appears visually correct.