1. MS Algebra A-S-ID-7 – Ch. 5.5a Find Slope Given Two Points
Mr. Deyo
Find Slope and Rate of Change

2. Title: 5.5a Find Slope Given Two Points
Date:
Learning Target
By the end of the period, I will find the slope of various linear equations and graphs when given two points.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.
Teacher Note: Graph paper helpful for this lesson.

3. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 5.5 Pg ) Section ______
TxtBk. Prob.#5-17 Odd Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

4. Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer:
How are the two images similar?
How are they different?
How can these two images be related to math?
IMAGE 1
IMAGE 2

5. Daily Warm-Up Exercises
For use with pages xxx–xxx
A cross-country skier traveled 14 miles in 3.5 hours. Use the formula d = r • t where d is distance, r is rate, and t is time, to find the average rate of speed.

6. Daily Warm-Up Exercises
For use with pages xxx–xxx
A cross-country skier traveled 14 miles in 3.5 hours. Use the formula d = r • t where d is distance, r is rate, and t is time, to find the average rate of speed.
ANSWER
4 mi/h

7. Vocabulary – Rate of Change
Slope
Rise
Run
Slope-Intercept Form
Point-Slope Form

8. Vocabulary Acquisition
Friendly Definition
Sketch
Wordwork
Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 1
Use Visuals
Introduce the word
Friendly Definition
Physical Representation
Use Cognates
Write friendly definition
Word List
Vocabulary Acquisition
DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing

9. y = mx + b Types of SLOPES of a Linear Equation Positive Negative Zero
Notes:
Types of SLOPES of a Linear Equation
y = mx + b
m = slope = rise/run = change in y / change in x
b = y-intercept = where graph crosses y-axis
x = independent variable, y = dependent variable
Positive
Negative
+ m
- m
Zero
Undefined
m = 0 (horizontal)
m = ?? (vertical)
Dividing by Zero

10. m= = = (3, 5) and (3, 1) - - x y Find a slope of a VERTICAL line
Problem A
Find a slope of a VERTICAL line
STEP 1)
You need two (2) points to find the slope:
(3, 5) and (3, 1)
STEP 2)
Make a table of points x y
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. - - m= = =
 denominator
 numerator

11. Problem A
Find a slope of a VERTICAL line
STEP 1)
You need two (2) points to find the slope:
(3, 5) and (3, 1)
STEP 2)
Make a table of points x y 3 5 1
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. 3
- 3 5
- 1 4 m=
=??
= 0
= 4
 denominator
 numerator
Division by zero is undefined.

12. m= = = (-2, 4) and (4, 4) - - x y Find a slope of a HORIZONTAL line
Problem B
Find a slope of a HORIZONTAL line
STEP 1)
You need two (2) points to find the slope:
(-2, 4) and (4, 4)
STEP 2)
Make a table of points x y
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. - - m= = =
 denominator
 numerator

13. m= = 0 6 = 6 = 0 (-2, 4) and (4, 4) 4 -2 4 - 4 -(-2) x y 4
Problem B
Find a slope of a HORIZONTAL line
STEP 1)
You need two (2) points to find the slope:
(-2, 4) and (4, 4)
STEP 2)
Make a table of points x y 4 -2
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. 4
-(-2) 4
- 4 6 m=
= 0
= 6
= 0
 denominator
 numerator

14. Storm Check (Think, Write, Discuss, Report)
What are the four types of slope?
The four types of slope are:
___________________ 2) ________________
3) _________________ 4) ________________

15. Storm Check (Think, Write, Discuss, Report)
What are the four types of slope?
The four types of slope are:
Positive ) Negative
3) Zero (horizontal) ) Undefined (vertical)

16. Title: 5.5a Find Slope Given Two Points
Date:
Learning Target
By the end of the period, I will find the slope of various linear equations and graphs when given two points.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.
Teacher Note: Graph paper helpful for this lesson.

17. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 5.5 Pg ) Section ______
TxtBk. Prob.#6-18 Even Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

18. y = mx + b Finding SLOPE of a Linear Equation m = - x1 - y1 y2 – y1
Notes:
Finding SLOPE of a Linear Equation
y = mx + b
m = slope = rise/run = change in y / change in x
b = y-intercept = where graph crosses y-axis
x = independent variable, y = dependent variable
STEP 1)
You need two (2) points to find the slope:
(x1, y1) and (x2, y2)
STEP 2)
Make a table of points x y x2 y2 x1 y1
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. x2
- x1 y2
- y1
y2 – y1
x2 – x1
m =
 denominator
 numerator

19. y = mx + b 3 m = 1 Finding SLOPE of a Linear Equation = 1 = 3 2 5 1
Example:
Finding SLOPE of a Linear Equation
y = mx + b
m = slope = rise/run = change in y / change in x
b = y-intercept = where graph crosses y-axis
x = independent variable, y = dependent variable
STEP 1)
You need two (2) points to find the slope:
(1, 2) and (2, 5)
STEP 2)
Make a table of points x y 2 5 1
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. 2
- 1 5
- 2 3 1
m =
= 1
= 3
 denominator
 numerator

20. m = = = = (-4, 2) and (2, 6) - x y - Find a positive slope Problem A
STEP 1)
You need two (2) points to find the slope:
(-4, 2) and (2, 6)
STEP 2)
Make a table of points x y
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. - -
m = = = =
 denominator
 numerator

21. 4 6 2 3 m = = = 6 = 4 (-4, 2) and (2, 6) 2 6 -4 -(-4) - 2 x y 2 6
Problem A
Find a positive slope
STEP 1)
You need two (2) points to find the slope:
(-4, 2) and (2, 6)
STEP 2)
Make a table of points x y 2 6 -4
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. 2
-(-4) 6
- 2 4 6 2 3
m = =
= 6
= 4
 denominator
 numerator

22. m = = = (3, 5) and (6, -1) - - x y Find a negative slope Problem B
STEP 1)
You need two (2) points to find the slope:
(3, 5) and (6, -1)
STEP 2)
Make a table of points x y
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. - -
m = = =
 denominator
 numerator

23. -6 m= =-2 3 = 3 = -6 (3, 5) and (6, -1) 6 -1 3 5 6 - 3 - 5 x y -1
Problem B
Find a negative slope
STEP 1)
You need two (2) points to find the slope:
(3, 5) and (6, -1)
STEP 2)
Make a table of points x y 6 -1 3 5
STEP 3)
Find the difference
Find the difference
STEP 4)
Make a fraction with the values from STEP 3. 6
- 3 -1
- 5 -6 3 m=
=-2
= 3
= -6
 denominator
 numerator

24. Storm Check (Think, Write, Discuss, Report)
How do you find the slope for a given linear equation? (3 or 4 sentences)
To find the slope for a given linear equation, I
have to ________________________________
___________________________________________
__________________________________________.

25. (0, 6) and (5, - 4) (5, 2) and (4, -1) x y x y
Find the slope of the line that passes through the points.
Guided Practice
(0, 6) and (5, - 4)
(5, 2) and (4, -1) x y x y

26. = -2 = 3 =5 =-10 = -1 = -3 = -10 5 = -3 -1 (0, 6) and (5, - 4)
Find the slope of the line that passes through the points.
Guided Practice
(0, 6) and (5, - 4)
(5, 2) and (4, -1) x y 5 -4 6 x y 4 -1 5 2
5 – 0 =5
-4 – 6
=-10
4 – 5
= -1
-1 – 2
= -3
ANSWER
ANSWER
= -10 5
= -3 -1
= -2
= 3

27. Vocabulary – Rate of Change
Slope
Rise
Run
Slope-Intercept Form
Point-Slope Form

28. Vocabulary Acquisition
Friendly Definition
Sketch
Wordwork
Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
DAY 1
Use Visuals
Introduce the word
Friendly Definition
Physical Representation
Use Cognates
Write friendly definition
Word List
Vocabulary Acquisition
DAY 3 and/or DAY 4
1. Review the word
Friendly Definition
Physical Representation
2. Show how the word works
Synonyms/antonym
Word Problems
Related words/phrases
Example/non-example
DAY 5
1. Review the word
Friendly definition
Physical Representation
3. Write a sentence
at least 2 rich words (1 action)
correct spelling
correct punctuation
correct subject/predicate agreement
clear and clean writing

29. Title: 5.5a Find Slope Given Two Points
Date:
Learning Target
By the end of the period, I will find the slope of various linear equations and graphs when given two points.
I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.
Teacher Note: Graph paper helpful for this lesson.

30. Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 5.5 Pg ) Section ______
TxtBk. Prob.#5-18 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of Contents
Date Description Date Due

31. Graph the function ( y = mx + b ) 2x – 5y = 10
Ticket OUT.
Step 1) Solve for y
Step 2) Plot y-intercept
Step 3) Plot the slope
2 or 3 times
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you. x y

32. 5 Graph the function ( y = mx + b ) 2x – 5y = 10 b = -2  (0, -2) x y
Ticket OUT.
ANSWER
Step 1) Solve for y
Step 2) Plot y-intercept
2x – 5y = 10
-2x = -2x
-5y = -2x +10
y = 2x -2 5
Step 1)
Step 3) Plot the slope
2 or 3 times
m = 2 5
(5, 0)
b = -2  (0, -2)
Step 2)
Turn to your partner and share your answer. Please use correct answer.
Partner B, please share what Partner A told you.
(0, -2)
Step 3) x y -5 -4 5
(-5, -4)