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

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?

Inclination and SlopeInclination:· 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…

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

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

What about the angle between 2 lines?

Angles between lines:

(Where m1 and m2 are the slopes of two non-perpendicular lines)

Ex. 2) Find the angle between the two following lines.

2x + y = 4x – y = 2

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.

Percent Road Grade

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

Assignment:

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