1. How can you use the slope of a line to describe the line?
3.3 Notes: Slopes of Lines
How can you use the slope of a line to describe the line?

2. Warm Up
Find the slope of the line that passes through the points (7,3) and (8,5).
Slope = 2

3. Vocab!
Slope
How to find slope given a line:
What does it mean if a slope of a line is zero?
What does it mean if a slope of a line is undefined?
Ratio of the change along the y-axis to the change along the x-axis between two points.
No Slope
Dividing by zero

4. Example 1 Find the slope of the given lines. a) c) 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = 8 −2 =−4
Start at the bottom right point, count up 8 spaces (rise) and over to the left 2 space (run).
𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = 7 8
Start at the bottom left point, count up 7 spaces (rise) and over to the right 8 spaces (run).

5. Vocab!   
Positive Slope 
Negative Slope
   
Zero Slope  
Undefined Slope

6. How to find slope given two points?
Vocab!
How to find slope given two points?
Slope Formula
Use the slope formula.
Coordinates (𝑥 1 , 𝑦 1 ), 𝑥 2 , 𝑦 2
𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1

7. Example 2 Find the slope of the lines that contain the given points:
(–3, 4), (2, 1) b) (–1, –3), (6, –3)
Use formula from previous slide.
1−4 2−−3 = −3 5 =− 3 5
Use formula from previous slide.
−3−−3 6−−1 = 0 7 =0

8. It is undefined because you cannot divide by 0.
Example 2 cont.
Find the slope of the lines that contain the given points: c) (2, –4), (5, 2) d) (3, 5), (3, 2)
Use formula from slide 6.
2−−4 5−2 = 6 3 =2
Use formula from slide 6.
2−5 3−3 = −3 0 =𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
It is undefined because you cannot divide by 0.

9. You Try! Try on your own first before you look at the answer
Find the slopes of line a, b, c and d. Line a: Line b:
6 , 4 & (8 , 2)
2−4 8−6 = −2 2 =−1
6 , 4 & (4 , 0)
0−4 4−6 = −4 −2 =2

10. Vocab! Slope of Parallel Lines Slope of Perpendicular Lines
Slope of Parallel Lines
      
Slope of Perpendicular Lines
How do you identify if two lines are parallel or perpendicular?
 Look at their line.
Two nonvertical lines have the same slope if and only if they are parallel.
Two nonvertical lines are perpendicular if and only if the product of their slope is -1.
Parallel
Perpendicular

11. Example 5
Determine whether 𝐹𝐺 and 𝐻𝐽 are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer.
1: Find slope of 𝐹𝐺
−1−−3 −2−1 = 2 −3 =− 2 3
2: Find slope of 𝐻𝐽
3−0 6−5 = 3 1 =3
3: Compare. Are the slopes the same (parallel)? No. Are the opposite reciprocal (perpendicular)? No.
Answer: Neither

12. Example 6
Determine whether 𝐴𝐵 and 𝐶𝐷 are parallel, perpendicular, or neither for A(–2, –1), B(4, 5), C(6, 1), and D(9, –2).
1: Find slope of 𝐴𝐵
5−−1 4−−2 = 6 6 =1
2: Find slope of 𝐶𝐷
−2−1 9−6 = −3 3 =−1
3: Compare. Are the slopes the same (parallel)? No. Are the opposite reciprocal (perpendicular)? Yes.
Answer: Perpendicular

13. How to graph a line parallel to a line containing two other points?
Find the slope of the line
Plot point of new line
Graph using new slope

14. Example 7
Graph the line that contains Q(5, 1) and is parallel to 𝑀𝑁 with M(–2, 4) and N(2, 1).
Find slope of 𝑀𝑁
1−4 2−−2 = −3 4
2. Plot new point
3. Using slope from 𝑀𝑁 find new point.

15. You Try!
Graph the line that contains R(2, –1) and is parallel to 𝑂𝑃 with O(1, 6) and P(–3, 1).
Find slope of 𝑂𝑃
1−6 −3−1 = −5 −4 = 5 4
2. Plot new point
3. Using slope from 𝑂𝑃 find new point.