1. Warm-up: Find the distance between (-2, 0), (3, 9)
Find the slope of the line passing through the points (-5, 1), (4, 10)
Find an equation of the line passing though (2, -5) with slope(m) = 7/2
HW: Pg. 795 – 796 (2 – 20 even, 26 – 34 even, 42 – 48 even)

2. 10.1 Lines
Objective:
Find the angle of inclination between two lines
Find the distance between a point and a line

3. 10.1 Lines
The Inclination of a nonhorizontal line is the positive angle theta measured counterclockwise from the x-axis to the line.
Acute angle
Obtuse angle

4. If a nonvertical line has inclination theta and slope m, then
m = tan
rise
or opposite  }
run or adjacent

5. Example) find the inclination of the line with slope 3/2. 2

6. Ex) Find the inclination of the line with slope -1/2. 2 1 -1

7. Ex) Find the inclination of the line given by 2x + 3y = 6
First, find the slope by solving for y.
Set m = tan
angle of inclination 3  1 -2
angle of inclination  180o – 33.69o = o

8. The angle between two lines.
If two non-perpendicular lines have slopes m1 and m2 , then the angle between the two lines is given by

9. Find the angle between the two lines.
Line 1: 2x - y - 4 = 0
Line 2: 3x + 4y -12 = 0
First, find the slope of the two lines.
m1 = and m2 = -3/4
Now substitute them into the equation.
Now take the
arctan of 11/2

10. The Distance Between a Point and a Line.
The distance between the point (x1, y1) and the line
given by Ax + By + C is

11. Ex) Find the distance between the point (4,1) and the line
y = 2x + 1
Note: first put the equation in general form.
-2x + y - 1 = 0

12. Ex) Find the area of a triangle with the points A(-3,0), B(0,4), C(5,2).
First, find the height.

13. To find the height, we need to find the equation of line AC.
So, find the slope of AC.
Point-slope form gives us:
Put this eq. in general form.
x - 4y + 3 = 0
Now find h using this equation and the point (0,4).

14. Now, using the distance formula between two points, find the
length of base AC.
Now, the area of a triangle is A = 1/2 (bh)

15. Sneedlegrit: Find the slope of the line with inclination   = 150 1
HW: Pg. 795 – 796 (2 – 20 even, 26 – 34 even, 42 – 48 even)