1. Warm-Up
1.) Using the point slope formula find the equation of a line with slope -2 , passing through the point (1, 3)
2.) Graph the line y = 3x + 4.
3.) Graph the line y = 3x - 2
4.) What is the slope of the lines in the equations for # 2, 3 above?

2. 4.3 Parallel and Perpendicular Lines
Objectives:
To determine whether the graphs of two equations are parallel or perpendicular

3. Parallel Lines
Parallel lines are lines in the same plane that never intersect.
Parallel lines have the same slope. -8 -6 -4 -2 2 4 6 8

4. Example 1 Determine whether these lines are parallel. y = 4x -6 and
The slope of both lines is 4.
So, the lines are parallel.

5. Example 2 Determine whether these lines are parallel. y – 2 = 5x + 4
and
-15x + 3y = 9
+15x x
y = 5x + 6
3y = x
y = 3 + 5x
y = 5x + 3
The lines have the same slope.
So they are parallel.

6. Example 3 Determine whether these lines are parallel. y = -4x + 2 and
+2y y
2y - 5 = 8x
2y = 8x + 5
Since these lines have different slopes, they are not parallel.

7. Example 4
Write the slope-intercept form of the equation of the line passing through the point (1, –6) and parallel to the line y = -5x + 3.
slope of new line = -5
y – y1 = m(x – x1)
y – (-6) = -5(x – 1)
y + 6 = -5x + 5
y = -5x - 1

8. Perpendicular Lines
Perpendicular lines are lines that intersect to form a 900 angle. -8 -6 -4 -2 2 4 6 8
The slopes of perpendicular lines are opposite reciprocals

9. Example 5 Determine whether these lines are perpendicular. and
y = -3x - 2
m = -3
Since the slopes are opposite reciprocals, the lines are perpendicular.

10. Example 6 Determine whether these lines are perpendicular. y = 5x + 7
and
y = -5x - 2
m = -5
Since the slopes are not opposite reciprocals, the lines are not perpendicular.

11. Example 7
Write an equation for the line containing (-3,-5) and perpendicular to the line y = 2x + 1.
First, we need the slope of the line y = 2x + 1.
m = 2
Second, we need to find out the slope of the line that is perpendicular to y = 2x + 1.
Lastly, we use the point-slope formula to find our equation.

12. Practice
Write an equation for the line containing the given point and perpendicular to the given line.
1) (0,0); y = 2x + 4
2) (-1,-3); x + 2y = 8