MS Algebra A-S-ID-7 Ch. 5.5a Find Slope Given Two Points. Mr. Deyo Find Slope and Rate of Change
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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: 1. How are the two images similar? 2. How are they different? 3. How can these two images be related to math?
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 1) Slope 2) Rise 3) Run 4) Slope-Intercept Form 5) Point-Slope Form
8 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork 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 Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing
9 Notes: Types of SLOPES of a Linear Equation y = mx + b Positive m = slope = rise/run = change in y / change in x b = y-intercept = where graph crosses y-axis x = independent variable, y = dependent variable Negative + m - m Zero Undefined m = 0 (horizontal) m =??(vertical) Dividing by Zero
10 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) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m=
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 STEP 3) 3-3 denominator x y = 0 = 4 numerator STEP 4) Make a fraction with the values from STEP 3. m= 4 0 =?? Division by zero is undefined.
12 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) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m=
13 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 4 STEP 3) 4 -(-2) denominator = 6 = 0 numerator STEP 4) Make a fraction with the values from STEP 3. m= 0 6 = 0
14 Storm Check (Think, Write, Discuss, Report) What are the four types of slope? The four types of slope are: 1) 2) 3) 4)
15 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)
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 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: (x 1, y 1 ) and (x 2, y 2 ) STEP 2) Make a table of points x y x 2 y 2 STEP 3) x 2 - x 1 x 1 y 1 y 2 - y 1 STEP 4) Make a fraction with the values from STEP 3. m = y 2 y 1 x 2 x 1 denominator numerator
19 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 STEP 3) 2-1 denominator x y = 1 = 3 numerator STEP 4) Make a fraction with the values from STEP 3. m = 3 1
20 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 STEP 3) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m = =
21 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 STEP 3) 2 -(-4) denominator = 6 = 4 numerator STEP 4) Make a fraction with the values from STEP 3. m = 4 = 2 6 3
22 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 STEP 3) - denominator = = - numerator STEP 4) Make a fraction with the values from STEP 3. m =
23 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 STEP 3) 6-3 denominator x y = 3 = -6 numerator STEP 4) Make a fraction with the values from STEP 3. m= -6 3 =-2
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 Guided Practice slope of the line that passes through the points. (0, 6) and (5, - 4) (5, 2) and (4, -1) x y x y
26 Guided Practice slope of the line that passes through the points. (0, 6) and (5, - 4) (5, 2) and (4, -1) x y x y =5 = ANSWER = -2 =-10 = -1 = -3-1 ANSWER = 3 = -3
27 Vocabulary Rate of Change 1) Slope 2) Rise 3) Run 4) Slope-Intercept Form 5) Point-Slope Form
28 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork 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 Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 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 ) Ticket OUT. 2x 5y = 10 Step 1) Step 2) Step 3) Solve for y Plot y-intercept Plot the slope 2 or 3 times x y
32 Graph the function ( y = mx + b ) Step 1) m = 2 5 Step 2) Step 3) 2x 5y = 10 2x 5y = 10-2x = -2x -5y = -2x x y = 2x -2 5 b = -2 (0, -2) y (-5, -4) (0, -2) Step 1) Step 2) Step 3) Ticket OUT. ANSWER Solve for y Plot y-intercept Plot the slope 2 or 3 times (5, 0)
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