1. Digits 5.3
(Day 1)
Types of Slopes
&
Rise/Run

2. Slope

3. Slope is the measure of the steepness of a line!
What is slope?
Slope is the measure of the steepness of a line!

4. Types of Slope
Imagine that you are walking to the right on a line.
A positive slope means that you are walking uphill.

5. Types of Slope
Imagine that you are walking to the right on a line.
A negative slope means that you are walking downhill.

6. Types of Slope
Imagine that you are walking to the right on a line.
Zero slope means that you are walking on level ground.

7. Types of Slope
Undefined slope is a vertical line. You can not walk up a vertical line. It is not possible. You would fall!
ouch!

13. Quadrant II Quadrant I Quadrant III Quadrant IV
Let’s review…
y-axis
Positive
Quadrant II
Quadrant I
Positive
Negative
x-axis
Negative
Quadrant III
Quadrant IV

14. How do you calculate slope?
Slope is a ratio and represented by the variable m.
One way to figure out slope is remember the ratio rise over run:

16. When you are given points on a line, you can calculate the slope by the following steps:
1. Write slope ratio.
2. Start at one point & find the vertical rise to the other point.
3. Start at the same point again and find the horizontal run.
4. Simplify

17. Steps to find the slope- Example 1
1. Write slope ratio.
2. Start at point A & find the vertical rise to point B. y
3. Find the horizontal run. • B x
4. Simplify • A

18. • • Example 2 Find the slope of the line. 1. Write slope ratio.
2. Start at either point. Find the vertical rise. y •
3. Find the horizontal run. • x

19.  NEVER change an improper fraction to a mix number. Why?
When simplifying slope….
NEVER change an improper fraction to a mix number. Why? 

20. zero ooooover the denominator
Example 3 Find the slope of the line.
1. Write slope ratio. y
2. Start at either point. Find the vertical rise.
3. Find the horizontal run. x • •
4. Simplify
zero ooooover the denominator
(zeroooooo slope)

23. zero unnnnder the numerator (unnnnndefined slope)
Example 4 Find the slope of the line.
1. Write slope ratio. y
2. Start at either point. Find the vertical rise. •
3. Find the horizontal run. x •
4. Simplify
zero unnnnder the numerator (unnnnndefined slope)

25. Student Companion
Pg. 106 Part 1
(Got it 1 & 2)

26. Digits 5.3
(Day 2)
Calculating Slope

27. Another way to calculate slope…
m =
run change in x
rise change in y =

28. change in y m = change in x
When you are given ordered pairs, you can calculate the slope by the following steps:
1. Stack the points
m =
run change in x
rise change in y =
change in y
2. Write the formula
change in x
3. Substitute numbers for your variables
4. Solve & simplify

29. 3. Substitute numbers for your variables
Example 1 Find the slope of the line that passes through the points (2,4) and (-1,5).
1. Stack the points
2. Write the formula
3. Substitute numbers for your variables
4. Solve & simplify

30. Example 2 Find the slope of the line that passes through the points
1. Stack the points
2. Write the formula
3. Substitute numbers for your variables
4. Solve & simplify

31. Zero oooooover the line
Example 3 Find the slope of the line that passes through the points
1. Stack the points
2. Write the formula
3. Substitute numbers for your variables
Zero oooooover the line
(zeroooooo slope)
4. Solve & simplify

32. Student Companion
Part 2 & 3

33. PRACTICE. Plot the points and draw the line that passes through them
PRACTICE. Plot the points and draw the line that passes through them. Without finding the slope, determine whether the slope is positive, negative, zero, or undefined.
3. (4,5) and (2,2) (6,1) and (– 4,1)
5. (2,2) and (–1,4) (3,6) and (3,–1)
Find the slope by walking the line. y y 8. 7. • • x x • •

34. PRACTICE. Plot the points and draw the line that passes through them
PRACTICE. Plot the points and draw the line that passes through them. Without finding the slope, determine whether the slope is positive, negative, zero, or undefined.
3. (4,5) and (2,2) (6,1) and (– 4,1)
5. (2,2) and (–1,4) (3,6) and (3,–1)
Find the slope by walking the line. y y 8. 7. • • x x • •

35. Practice Problems
Find the slope using the slope formula.
(4,5) and (2,2) ) (6,1) and (– 4,1)
(2,2) and (–1,4) ) (3,6) and (3,–1)
5. (2,-1) and (3,4) ) (-3,-7) and (3,-7)
undefined 5

36. Finding Slope from a table

37. Watch Video:

38. Now you try…
Watch Video:

39. Challenging Questions

40. United Streaming Video

41. Zero unnnnnder the line is unnnnndefined.
Okay, so you use the slope formula and you generate the fraction .
Zero unnnnnder the line is unnnnndefined.
What is the answer?
Undefined

42. Zero oooooover the line is
You use the slope formula and generate a fraction like .
What is the answer?
Zero oooooover the line is
zeroooooo.

43. Zero unnnnder the line is unnnnndefined.
Example 3 Find the slope of the line that passes through the points
Zero unnnnder the line is unnnnndefined.