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

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.

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 Contents Date Description Date Due

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

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.

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

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

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

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

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

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.

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

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

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

Storm Check (Think, Write, Discuss, Report) What are the four types of slope? The four types of slope are: Positive 2) Negative 3) Zero (horizontal) 4) Undefined (vertical)

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.

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 Contents Date Description Date Due

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

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

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

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

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

-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

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 ________________________________ ___________________________________________ __________________________________________.

(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

= -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

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

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

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.

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 Contents Date Description Date Due

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

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 -5 -5 -5 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)