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MS Algebra A-S-ID-7 – Ch. 5.5aFind Slope Given Two Points
Mr. Deyo
Find Slope and Rate of Change
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.
Learning Target
Title: 5.5a Find Slope Given Two Points Date:
Teacher Note: Graph paper helpful for this lesson.
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 5.5 Pg. 286-289 3) Section ______
TxtBk. Prob.#5-17 Odd Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
Storm Check (Think, Write, Discuss, Report)
Questions on which to ponder and answer:1. How are the two images similar?
2. How are they different?
3. How can these two images be related to math?
For use with pages xxx–xxxDaily Warm-Up Exercises
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.
For use with pages xxx–xxxDaily Warm-Up Exercises
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
1) Slope
2) Rise
3) Run
4) Slope-Intercept Form
5) Point-Slope Form
Vocabulary – Rate of Change
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
Friendly DefinitionSketch
Wordwork Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
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
DAY 1
1. Use Visuals
2. Introduce the word
Friendly Definition
Physical Representation
3. Use Cognates
4. Write friendly definition
5. Physical Representation
Word List1.2.3.4.
Notes: Types of SLOPES of a Linear Equation
y = mx + bm = slope = rise/run = change in y / change in xb = y-intercept = where graph crosses y-axisx = independent variable, y = dependent variable
Positive
Undefined
Negative
Zero
+ m - m
m = 0 (horizontal) m = ??(vertical)Dividing by Zero
STEP 1)You need two (2) points to find the slope:
(3, 5) and (3, 1)
x y
STEP 4)Make a fraction with the values from STEP 3.-
Find the difference
-
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
m== =
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)
x y
3 5
3 1
STEP 4)Make a fraction with the values from STEP 3.
3
- 3
Find the difference
5
- 1
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
m== 0 = 4
Problem A Find a slope of a VERTICAL line
40
=??Division by zero is undefined.
STEP 1)You need two (2) points to find the slope:
(-2, 4) and (4, 4)
x y
STEP 4)Make a fraction with the values from STEP 3.-
Find the difference
-
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
m== =
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)
x y
4 4
-2 4
STEP 4)Make a fraction with the values from STEP 3.
4
-(-2)
Find the difference
4
- 4
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
m== 6 = 0
Problem B Find a slope of a HORIZONTAL line
06
= 0
Storm Check (Think, Write, Discuss, Report)
What are the four types of slope?
The four types of slope are:
1) ___________________ 2) ________________
3) _________________ 4) ________________
Storm Check (Think, Write, Discuss, Report)
What are the four types of slope?
The four types of slope are:
1) Positive 2) Negative
3) Zero (horizontal) 4) Undefined (vertical)
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.
Learning Target
Title: 5.5a Find Slope Given Two Points Date:
Teacher Note: Graph paper helpful for this lesson.
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 5.5 Pg. 286-289 3) Section ______
TxtBk. Prob.#6-18 Even Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
Notes: Finding SLOPE of a Linear Equation
y = mx + bm = slope = rise/run = change in y / change in xb = y-intercept = where graph crosses y-axisx = independent variable, y = dependent variable
STEP 1)You need two (2) points to find the slope:
(x1, y1) and (x2, y2)
x y
x2 y2
x1 y1
STEP 4)Make a fraction with the values from STEP 3.
x2
- x1
Find the difference
y2
- y1
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
y2 – y1
x2 – x1m =
Example: Finding SLOPE of a Linear Equation
y = mx + bm = slope = rise/run = change in y / change in xb = y-intercept = where graph crosses y-axisx = independent variable, y = dependent variable
STEP 1)You need two (2) points to find the slope:
(1, 2) and (2, 5)
x y
2 5
1 2
STEP 4)Make a fraction with the values from STEP 3.
2
- 1
Find the difference
5
- 2
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
31
m == 1 = 3
STEP 1)You need two (2) points to find the slope:
(-4, 2) and (2, 6)
x y
STEP 4)Make a fraction with the values from STEP 3.-
Find the difference
-
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
m == =
Problem A Find a positive slope
=
STEP 1)You need two (2) points to find the slope:
(-4, 2) and (2, 6)
x y
2 6
-4 2
STEP 4)Make a fraction with the values from STEP 3.
2
-(-4)
Find the difference
6
- 2
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
46
m == 6 = 4
Problem A Find a positive slope
= 23
STEP 1)You need two (2) points to find the slope:
(3, 5) and (6, -1)
x y
STEP 4)Make a fraction with the values from STEP 3.-
Find the difference
-
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
m == =
Problem B Find a negative slope
STEP 1)You need two (2) points to find the slope:
(3, 5) and (6, -1)
x y
6 -1
3 5
STEP 4)Make a fraction with the values from STEP 3.
6
- 3
Find the difference
-1
- 5
STEP 2)Make a table of points
STEP 3)Find the difference
denominator numerator
m== 3 = -6
Problem B Find a negative slope
-63
=-2
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 ________________________________
___________________________________________
___________________________________________
__________________________________________.
Guided PracticeFind the slope of the line that passes through the points.
(0, 6) and (5, - 4) (5, 2) and (4, -1)
x y x y
Guided Practice
ANSWER
Find the slope of the line that passes through the points.
(0, 6) and (5, - 4) (5, 2) and (4, -1)
ANSWER
x y
5 -4
0 6
x y
4 -1
5 2
= -2
5 – 0
=5-4 – 6
=-10= -10
5= 3
4 – 5
= -1-1 – 2
= -3= -3
-1
1) Slope
2) Rise
3) Run
4) Slope-Intercept Form
5) Point-Slope Form
Vocabulary – Rate of Change
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
Friendly DefinitionSketch
Wordwork Sentence
DAY 2
1. Review word
Friendly Definition
Physical Representation
2. Draw a sketch
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
DAY 1
1. Use Visuals
2. Introduce the word
Friendly Definition
Physical Representation
3. Use Cognates
4. Write friendly definition
5. Physical Representation
Word List1.2.3.4.
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.
Learning Target
Title: 5.5a Find Slope Given Two Points Date:
Teacher Note: Graph paper helpful for this lesson.
Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder?
2) Section 5.5 Pg. 286-289 3) Section ______
TxtBk. Prob.#5-18 ALL Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder?
Table of ContentsDate Description Date Due
Ticket OUT. Graph the function ( y = mx + b )
2x – 5y = 10
x y
Step 1) Solve for yStep 2) Plot y-interceptStep 3) Plot the slope
2 or 3 times
Ticket OUT. Graph the function ( y = mx + b )
2x – 5y = 102x – 5y = 10-2x = -2x
-5y = -2x +10-5 -5 -5
y = 2x -25
Step 1)
Step 2)
ANSWER
(0, -2)
(5, 0)
x y
-5 -4
5 0
Step 1) Solve for yStep 2) Plot y-interceptStep 3) Plot the slope
2 or 3 times
m = 25
b = -2 (0, -2)
(-5, -4)
Step 3)