Mr. Deyo Solving Problems by Writing Equations in Point-Slope Form MS Algebra A-F-IF-7 – Ch. 6.3a Solving Problems by Writing Equations in Point-Slope Form Mr. Deyo Solving Problems by Writing Equations in Point-Slope Form

Title: 6.3a Apply Point-Slope Form to Solve Problems Date: Learning Target By the end of the period, I will apply the slope formula and the point-slope form to write equations and solve problems. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 6.3 Pg. 343-344 3) Section ______ TxtBk.Prob.#3-11 Odd,27-35 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 Step 1: Find the slope between 2 points Daily Warm-Up Exercises Step 2: Find the value of b using m and 1 point For use with pages xxx–xxx Step 3: Write general y = mx + b equation A carnival charges an entrance fee and a ticket fee. One person paid $27.50 and bought 5 tickets. Another paid $45.00 and bought 12 tickets. How much will 22 tickets cost? Tickets Costs 5 $27.50 12 $45.00 22 $

Daily Warm-Up Exercises Step 1: Find the slope between 2 points Daily Warm-Up Exercises Step 2: Find the value of b using m and 1 point For use with pages xxx–xxx Step 3: Write general y = mx + b equation A carnival charges an entrance fee and a ticket fee. One person paid $27.50 and bought 5 tickets. Another paid $45.00 and bought 12 tickets. How much will 22 tickets cost? Tickets Costs 5 $27.50 12 $45.00 22 Step 1 45 – 27.5 17.5 2.5 m = = = $70 12 - 5 7 ANSWER Step 2 45 = 2.5(12) + b 45 = 30 + b 15 = b Step 3 y = mx + b y = 2.5(22) + 15 y = 55 + 15 y = 70

Vocabulary Slope y-intercept 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

How To Get To Point-Slope Form Notes: Given One Point & SLOPE Step 1) Plug m and one point into y – Y1 = m(x – X1) x y X1 Y1 Step 2) Solve for y (if you want slope-intercept form)

Problem A Write an equation in point-slope form Write an equation in point-slope form of the line that passes through the point (-1, 4) and has a slope of -2. x1, y1 m

Problem A Write an equation in point-slope form Write an equation in point-slope form of the line that passes through the point (-1, 4) and has a slope of -2. x1, y1 m y – 4 = -2(x + 1) ANSWER

Problem B Write an equation in point-slope form Write an equation in point-slope form of the line that passes through the point (4, -3) and has a slope of 2. x1, y1 m

Problem B Write an equation in point-slope form Write an equation in point-slope form of the line that passes through the point (4, -3) and has a slope of 2. x1, y1 m y + 3 = 2(x - 4) ANSWER

m = How To Get To Point-Slope Form Y2 – Y1 X2 – X1 X1 Y1 X2 Y2 Notes: Given Two Points x y X1 Y1 X2 Y2 Step 1) Make a table Use the two points to calculate SLOPE (m) Y2 – Y1 m = X2 – X1 Step 2) Plug m and one point into y – Y1 = m(x – X1) Step 3) Solve for y (if you want slope-intercept form)

m = = y – y1 = m(x – x1) y – y2 = m(x – x2) Problem A Given two points, write an equation in point-slope form Write an equation in point-slope form of the line that passes through the points (2, 3) and (4, 4). x1, y1 x2, y2 Step 1: Find the slope between 2 points x y m = = Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form y – y1 = m(x – x1) y – y2 = m(x – x2)

m = = y – y1 = m(x – x1) y – 3 = ½ (x – 2) y – y2 = m(x – x2) Problem A Given two points, write an equation in point-slope form Write an equation in point-slope form of the line that passes through the points (2, 3) and (4, 4). x1, y1 x2, y2 Step 1: Find the slope between 2 points x y 4 2 3 4 - 3 1 m = = 4 - 2 2 Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form y – y1 = m(x – x1) y – 3 = ½ (x – 2) y – y2 = m(x – x2) y – 4 = ½ (x – 4) 2 Correct ANSWERS

m = = y – y1 = m(x – x1) y – y2 = m(x – x2) Problem B Given two points, write an equation in point-slope form Write an equation in point-slope form of the line that passes through the points (-1, 3) and (1, 1). x1, y1 x2, y2 Step 1: Find the slope between 2 points x y m = = Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form y – y1 = m(x – x1) y – y2 = m(x – x2)

m = = = -1 y – y1 = m(x – x1) y – 3 = -1 (x + 1) y – y2 = m(x – x2) Problem B Given two points, write an equation in point-slope form Write an equation in point-slope form of the line that passes through the points (-1, 3) and (1, 1). x1, y1 x2, y2 Step 1: Find the slope between 2 points x y 1 -1 3 1 - 3 -2 m = = = -1 1- (-1) 2 Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form y – y1 = m(x – x1) y – 3 = -1 (x + 1) y – y2 = m(x – x2) y – 1 = -1(x – 1) 2 Correct ANSWERS

Storm Check (Think, Write, Discuss, Report) If you are given two points, how can you create a linear equation that is in point-slope form? (2-3 sentences) When given two points, I can create a linear equation in point-slope form by ___________________ _______________________________________________ ______________________________________________.

Vocabulary Slope y-intercept Data Pair Slope-Intercept Form Point-Slope Form

Title: 6.3a Apply Point-Slope Form to Solve Problems Date: Learning Target By the end of the period, I will apply the slope formula and the point-slope form to write equations and solve problems. I will demonstrate this by completing Four-Square Notes and by solving problems in a pair/group activity.

Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 6.3 Pg. 343-344 3) Section ______ TxtBk.Prob.#3-11 Odd,27-35 Odd Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

Ticket OUT. Write an equation of the line that passes through the points (1, 5) and (4, –1). Step 1: Find the slope between 2 points x y Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you.

-2 m = = = y – y1 = m(x – x1) y – 5 = -2(x – 1) y – y2 = m(x – x2) Ticket OUT. Write an equation of the line that passes through the points (1, 5) and (4, –1). Step 1: Find the slope between 2 points x y 4 -1 1 5 -1 - 5 -6 -2 m = = = 4 - 1 3 Step 2a: Plug m and 1st point into Point-Slope Form Step 2b: Plug m and the 2nd point into the Point-Slope Form Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you. y – y1 = m(x – x1) y – 5 = -2(x – 1) y – y2 = m(x – x2) y + 1 = -2(x – 4)