Chp 10.1
Lines (Page
Higher
Mathematics
Objective:
To find the
inclination
of a line and
angle
between
two lines.
Bellwork
1.
On a certain day, the probability of rain in
Seattle is 75% and 5%
in Death Valley. Assume the chance of rain in the two cities is
independent. What is the probability it will NOT rain in either city?
2.
Find the sum of the geometric series.
25, 5, 1,….
Functions Recall all the most used functions in this course.
Conics A conic section or simple conic is the intersection of a plane and a double
napped cone.
General The general equation for all conics is
Equation
Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Inclination The inclination of a nonhorizontal line is the positive angle θ (less than π)
of a Line measured counterclockwise from the x-axis to the line.
Horizontal Line
Vertical Line
Positive Line
Negative Line
If a nonvertical line has inclination θ and slope m,
then m = tanθ or tan-1 = θ.
Example 1 a. Find the inclination of the line 2x + 3y = 6.
b. Find the slope of the line with 


4
.
Angle If two nonperpendicular lines have slopes m1 and m2, the angle between
Between the two lines is
m  m1
Two Lines
tan   2
1  m1m2
Example 2 Find the angle between the two lines.
2x – y – 4 = 0
3x + 4y – 12 = 0
Distance The distance between the point (x1, y1) and the line
Between Ax + By + C = 0 is
Ax1  By1  C
a Point
d

And Line
A2  B 2
Example 3 Find the distance between the point (4, 1) and the line y = 2x + 1.