What you’ll learn
Write equations of perpendicular lines.
Key idea
Perpendicular finite slopes multiply to negative one; changing slope alone does not ensure point membership.
Require slope product -1 and point membership; copied output can have correct slope but miss the point.
Worked example
Enter the exact value or ordered values in the format requested below.
A coordinate-map reference path is y=-5x+3; a perpendicular path must pass through (15,-1). Write the full target equation with exact coefficients.
- For finite nonzero slopes the negative reciprocal is 1/5; -5×(1/5)=-1.
- Substitute the designated point: -1=(1/5)(15)+b, hence b=-4. Equation y=1/5x-4 satisfies slope and point constraints.
Answer: y=1/5x-4
Quick Check
Choose which candidate representation satisfies the requirements of 'Write equations of perpendicular lines' and justify the choice.
A coordinate-map reference path is y=-5x+3; a perpendicular path must pass through (5,2). Choose with BOTH slope-product and point evidence.