7.6 Normal
Form of a Line
Linear Equations
What are different ways (forms) to write an equation
of a line?
• Normal Line: A line perpendicular to another line or
curve
Normal Form
x cos φ + ysinφ = p = 0
p: length of normal line to origin
φ: positive angle between normal line and x-axis
To change from standard form to normal form,
divide by
± 𝐴2 + 𝐵 2
(use opposite sign as C)
Change to normal form:
2) 6x + 8y + 3 =0
3) What is the length of the above normal line?
4) What is the angle to the x-axis?
Change to normal form:
5) –x + 4y – 6 =0
6) What is the length of the above normal
line?
7) What is the angle to the x-axis?