1. 2.4.2 – Parallel, Perpendicular Lines

2. We know how to quickly graph certain linear equations
Y = mx + b
Slope-intercept
Y-intercept as a starting point; slope to find a second point
Ax + by = c
Standard Form
Use the x and y intercepts as the two points

3. Now, we will compare two lines/equations and their graphs
Two lines may be:
1) Parallel
2) Perpendicular
3) Neither

4. Parallel Lines
Given two lines, they are considered parallel if and only if they have the same slope; m1 = m2
The lines never intersect; run off in the same direction
“Air” between them

5. Example. Tell whether the following lines are parallel or not.
1) y = 3x + 4, y – 3x = 10
2) -4x + y = -6, y = 4x
3) y – x = 1, y = -x

6. Example. Graph the equation y = 3x + 4
Example. Graph the equation y = 3x + 4. Then, graph a line that is parallel and passes through the point (1, 1).

7. Example. Graph the equation y = -x + 5
Example. Graph the equation y = -x + 5. Then, graph a line that is parallel and passes through the point (1, 1).

8. Perpendicular Lines
Two lines are perpendicular, if and only if, their slopes are negative reciprocals OR their product is -1
OR m1(m2) = -1
Graphically, two perpendicular lines intersect at a 90 degree angle

9. Example. Tell whether the following lines are perpendicular, parallel, or neither.
1) y = 3x + 4, y = (-1/3)x – 5
2) y = 4x – 5, y = x
3) y = (x/2) – 9, y + (2/x) = -6
4) y = x – 1, y = -x

10. Example. Graph the equation y = 3x + 4
Example. Graph the equation y = 3x + 4. Then, graph a line that is perpendicular and passes through the point (1, 1).

11. Example. Graph the equation y = -x + 5
Example. Graph the equation y = -x + 5. Then, graph a line that is perpendicular and passes through the point (1, 1).

12. Horizontal and Vertical Lines
Horizontal Lines = lines of the form y = a; must have a “y-intercept”
Vertical Lines = lines of the form x = a; must have a “x-intercept”
General Rule; must be able to see the line, so cannot draw a line on top of the axis

13. Example. Graph the equation x = 3.

14. Example. Graph the equation y = -4.

15. Assignment
Pg. 91
33-49 odd, 50-53, 60, 62, 69, 70