This document provides an overview of slope, parallel lines, and perpendicular lines. It defines key concepts such as slope, slope-intercept form, standard form, and point-slope form. It also discusses how to calculate slope and classify lines based on their slopes. The document notes that parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other. It provides examples of finding equations of parallel and perpendicular lines.

1. Slope, Parallel and
Perpendicular Lines
.

2. Try these…..Review
1.Find the reciprocal of each fraction
a.
1
2
b.
4
3
c.
1
−
3
d.
5
−
2
2.Find the slope and y-intercept of each equation
5
a. y = x + 4
4
5
b. y = x − 8
3
c. y = 6 x
d. y = 6 x + 2

3. Quick Review/Preview
1. What is the Slope-Intercept Form?
y = mx + b
2. What is the Standard Form?
Ax + By = C
3. What is the Point-Slope Form?
y – y1 = m(x – x1)
4. Find the “negative reciprocal” of each fraction
2
3 7
1 2
4 3
5
a.
b. −
c. −
−
= 2 d. −
5
7 3
2 1
3 4
2

4. Overview
How to calculate a slope
 Parallel Lines and Perpendicular Lines
 Write equations for each type of lines


5. Notes
Finding the Slope of a Line
Slope is found using the equation m= y2 -y1.
x2 -x1
The coordinates for the points on the graph are plugged
into the equation above. The equation is then solved and
the remaining solution is the slope.
Example:
Let (x1, y1) = (-3, 5) and (x2, y2) = (2, 1)

6. Notes
Classifying Lines Using Slope




A line with a positive slope rises from left to right. (m>0)
A line with a negative slope falls from left to right. (m<0)
A line with a slope of zero is horizontal. (m=0)
A line with an undefined slope is vertical. (m is undefined.)
Positive Slope
Negative Slope
Zero Slope
Undefined Slope

7. Notes Continued
Slopes of Parallel and Perpendicular Lines
Parallel Lines The lines are parallel if and only if they have the same
slope.
m1 = m2
Perpendicular Lines The lines are perpendicular if and only if their
slopes are negative reciprocals of each other
m1 = - 1 or m1m2 = -1
m2
Parallel Lines
Perpendicular Lines

8. Parallel Lines
Parallel Lines - lines that never intersect
What is the slope of the
red line?
1/2
What is the slope of the
blue line?
1/2
Parallel Lines have the same slope!

9. Parallel Lines
Determine if the lines are parallel
1
1. 2 x + 6 y = 12 and y = − x + 5
3
2x + 6y = 12
6y = -2x + 12
1
y = − x+2
3
yes

10. Parallel Lines
Determine if the lines are parallel
3
2. 6 x + 8 y = −24 and y = x − 3
4
6x + 8y = -24
8y = -6x – 24
3
y = − x +3
4
No

11. Parallel Lines
Determine if the lines are parallel
2
3. 4 x + 6 y = −2 and y = x −8
3
4x + 6y = -2
6y = -4x – 2
2
1
y = − x−
3
3
No

12. Perpendicular Lines
Perpendicular Lines – lines that intersect to form
right angles
What is the slope of the
red line?
-1/4
What is the slope of the
blue line?
4/1
Perpendicular Lines have negative reciprocal slope!

13. Perpendicular Lines
What is the slope of the perpendicular line?
2
7. y = x − 8
5
1
8. y = − x
5
9. y = −2 x − 7
-5/2
5/1 = 5
1/2

14. Equations of Perpendicular Lines
10. Find the equation of the line that
contains (0, -2) and is perpendicular to
y = 5x + 3
1
m=−
5
1
y+2=− x
5

15. Equations of Perpendicular Lines
11. Find the equation of the line that
contains (1, 8) and is perpendicular to
3
y = x+1
4
4
m =− 3
4
y − 8 = − ( x − 1)
3

16. Equations of Perpendicular Lines
12. Find the equation of the line that
contains (2, -3) and is perpendicular to
1
y = − x+ 6
2
m=2
y + 3 = 2(x – 2)

17. Perpendicular Lines
13. Determine if the lines are perpendicular:
2
y = x + 1 and 3 y + 2 x = 4
3
3y + 2x = 4
3 y = −2 x + 4
2
4
y =− x+
3
3
No
14. Determine if the lines are perpendicular:
4
y = x − 5 and 4 y + 3 x = 9
3
4y + 3 x = 9
4 y = −3 x + 9
y =−
3
9
x+
4
4
Yes

18. Challenge
What is the slope of the line that is parallel
to x = 4?
undefined
 What is the slope of the line that is
perpendicular to x = 4?
zero
