Calculates the equation of a line perpendicular to a given line and passing through a specified point. The calculator determines the slope of the perpendicular line, and then uses the point-slope form to find the equation in slope-intercept form (y = mx + b).
Start with your values, or try a preset.
Enter Slope of the Original Line (m), X-coordinate of the Point (x₁), and Y-coordinate of the Point (y₁) in the units shown.
Read Slope of the Perpendicular Line (m⟂), Y-intercept of the Perpendicular Line (b), and Equation of the Perpendicular Line (y = mx + b) in the results panel. Results update as you change the inputs.
Choose a preset to load an example, then adjust the values for your situation.
See the inputs and their calculated results.
Slope of the Original Line (m): 2; X-coordinate of the Point (x₁): 1; Y-coordinate of the Point (y₁): 3
Slope of the Perpendicular Line (m⟂): -0.5; Y-intercept of the Perpendicular Line (b): 3.5; Equation of the Perpendicular Line (y = mx + b): y = -0.5x + 3.5
Slope of the Original Line (m): -3; X-coordinate of the Point (x₁): 2; Y-coordinate of the Point (y₁): -1
Slope of the Perpendicular Line (m⟂): 0.3333333333; Y-intercept of the Perpendicular Line (b): -1.666666667; Equation of the Perpendicular Line (y = mx + b): y = 0.3333333333333333x + -1.6666666666666665
Slope of the Original Line (m): 0.5; X-coordinate of the Point (x₁): -2; Y-coordinate of the Point (y₁): 4
Slope of the Perpendicular Line (m⟂): -2; Y-intercept of the Perpendicular Line (b): 0; Equation of the Perpendicular Line (y = mx + b): y = -2x + 0
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