Finding the inclination of a line and also the angle between two lines

1. 10.1 Tangent Lines
Objective:
1) Find the angle of inclination and
slope of a line.
2) Find the angle between 2 lines.
Standard: Trigonometry 7.0

2. Warm-up:
1) Find the slope of the line containing the
two points (–4, 1) and (3, 6).
2) What is the angle this line makes with
the x-axis?

3. Inclination and Slope
Inclination:
· The ___________ _________ less than ___
measured _________________ from the x-
axis to the line.
Slope:
· If a non-vertical line has an inclination
of θ and a slope of m, then…

4. Ex. 1) Find the inclination.
Find the angle of inclination of the line
given by 5x–7y+3=0.

5. Ex. 1b) Find the inclination of 3x+4y=7.

6. What about the angle
between 2 lines?

7. Angles between lines:
(Where m1 and m2 are the slopes
of two non-perpendicular lines)

8. Ex. 2) Find the angle between the two
following lines.
2x + y = 4
x–y=2

9. Ex. 3) Application:
A straight road rises with the inclination of
0.20 radians from the horizontal. Find the
slope of the road and the change in
elevation of a 2-mile stretch of the road.

10. Percent Road Grade

11. Ex. 4) Find the equation of the line with an
inclination of 120° and through the point
(-3, 5).

12. Assignment:
#5 p. 732
#9-31 (odd),
51, 53, 56