Find The Equation of the Line Perpendicular to Another Line

Find the equation of a line that is perpendicular to a given line and passes through a specified point. Generate random problems, see detailed step-by-step solutions, and visualize both lines on a graph.

📐 Perpendicular Line Through a Point

Find line perpendicular to \( a_1x + b_1y = c_1 \) through point \( (x_0, y_0) \)

Line: \( 2x - y = 3 \), Point: \( (1, 2) \)
Find the equation of the line perpendicular to the given line through the point.

📖 Step-by-Step Solution

STEP 1: Write the given line in slope-intercept form (y = mx + b)
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STEP 2: Identify the slope m₁ of the given line
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STEP 3: Find the slope m₂ of the perpendicular line (negative reciprocal)
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STEP 4: Write the equation in point-slope form
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STEP 5: Convert to slope-intercept form
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📊 Graphical Visualization
Given line: Blue | Perpendicular line: Green | Given point: Red

Adjust axis scale to see both lines clearly. Perpendicular lines intersect at a right angle.