Chapter 7.6 Normal Form of a Linear Equation
Obj: Write a linear equation in normal form
You are familiar with several forms for the equation of a line. These include
slope-intercept form, point-slope form, and standard form. The usefulness of
each form in a particular situation depends on how much relevant
information each form provides upon inspection. The normal form uses
trigonometry to provide information about the line.
Normal – a line that is perpendicular to another line, curve,
or surface.
The normal line of a linear equation can be written in terms
of trig functions.
Normal Form
Changing the Standard Form to the Normal Form
Write the standard form of the equation for the line given 𝜌 (the measure of the normal),
and 𝜑 (the angle that the normal makes with the positive 𝑥 − 𝑎𝑥𝑖𝑠)
1) 𝑝 = 3 𝑢𝑛𝑖𝑡𝑠
𝜙 = 60°
Write the standard form of the equation for the line given 𝜌 (the measure of the normal),
and 𝜑 (the angle that the normal makes with the positive 𝑥 − 𝑎𝑥𝑖𝑠)
2) 𝑝 = 8 𝑢𝑛𝑖𝑡𝑠
𝜙 = 45°
Write the standard form of the equation for the line given 𝜌 (the measure of the normal),
and 𝜑 (the angle that the normal makes with the positive 𝑥 − 𝑎𝑥𝑖𝑠)
3) 𝑝 = 2 𝑢𝑛𝑖𝑡𝑠
𝜙 = 150°
Write the standard form equation in normal from. Find 𝑝 𝑎𝑛𝑑 𝜙
1) 2𝑥 − 5𝑦 + 3 = 0
Write the standard form equation in normal from. Find 𝑝 𝑎𝑛𝑑 𝜙
2) 2𝑥 + 𝑦 − 5 = 0
Write the standard form equation in normal from. Find 𝑝 𝑎𝑛𝑑 𝜙
3) 3𝑥 + 4𝑦 − 1 = 0
Homework Ch 7-6 – p396/ 13-25 odds