Math 1 · Unit 4 · Lesson 2 · part 4 of 6
Write a perpendicular line through a point
The skill: given a line, write the equation of a line perpendicular to it through a given point .
Write a perpendicular line through a point
The skill: given a line, write the equation of a line perpendicular to it through a given point. Two moves again, and only the first is new.
- 1Take the negative reciprocal of the slopeRead m off the given line (rewrite into y = mx + b first if needed). Flip it and change the sign. That is the new m.
- 2Use the point to find the new bPut the point's x and y into y = mx + b with the new m, and solve for b. Write y = mx + b.
Worked: perpendicular to y = 2x + 1 through (4, 3)
m = 2 = 21. Flip: 12. Change the sign: new m = −12.
Put in (4, 3): 3 = −12 × 4 + b, so 3 = −2 + b, so b = 5.
y = −12x + 5. Check the slopes: 2 × (−12) = −1. Square corner.
Worked: perpendicular to y = −34x − 2 through (−3, 1)
m = −34. Flip: −43. Change the sign: new m = 43.
Put in (−3, 1): 1 = 43 × (−3) + b, so 1 = −4 + b, so b = 5.
y = 43x + 5. Check: −34 × 43 = −1.