MS Algebra A-F-IF-7 – Ch. 6.5b Write Equations of Perpendicular Lines Mr. Deyo Write Equations of Perpendicular Lines

Title: 6.5b Write Equations of Perpendicular Lines Date: Learning Target By the end of the period, I will write equations of perpendicular lines. 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 6.5 Pg. 357-359 3) Section ______ TxtBk.Prob.#12,22,23,24,25,26 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 You play tennis at two clubs. The total cost C (in dollars) to play for time T (in hours) and rent equipment is given by C = 15T + 23 at one club and C = 15T + 17 at the other. What is the difference in total cost after 4 hours of play?

Daily Warm-Up Exercises For use with pages xxx–xxx You play tennis at two clubs. The total cost C (in dollars) to play for time T (in hours) and rent equipment is given by C = 15T + 23 at one club and C = 15T + 17 at the other. What is the difference in total cost after 4 hours of play? ANSWER $6

Vocabulary Slope Parallel Lines Perpendicular Lines 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

= m1 -1 1 m2 (m1)(m2) = -1(1) Perpendicular Lines m1 = m2 = Notes: Two different non-vertical lines in the same plane are perpendicular if their slopes are negative reciprocals. m1 -1 1 m2 Y2 – Y1 Y3 – Y4 m1 = m2 = = X2 – X1 X3 – X4 y – Y1 = m1(x – X1) y = m1x + b y – Y3 = m2(x – X3) y = m2x + b (m1)(m2) = -1(1)

Write an equation of a perpendicular line Step 1: Identify the slope. Find the Negative Reciprocal. Problem A Step 2: Find the y-intercept Step 3: Write general y = mx + b equation Write an equation of the line that passes through (4, -5) and is perpendicular to the line y = 2x + 3

Write an equation of a perpendicular line Step 1: Identify the slope. Find the Negative Reciprocal. Problem A Step 2: Find the y-intercept Step 3: Write general y = mx + b equation Write an equation of the line that passes through (4, -5) and is perpendicular to the line y = 2x + 3 SOLUTION STEP 1 Identify the slope. The graph of the given equation has a slope of 2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (4, -5) is -1/2. STEP 2 Find the y-intercept. Use the slope and the given point. Write slope-intercept form. = y + mx b = 5 + b – 2 1 ( ) 4 Substitute –(1/2) for m, 4 for x, and -5 for y. = 3 b – Solve for b. STEP 3 Write an equation. = y + mx b Write slope-intercept form. = y 3 2 1 – x Substitute –(1/2) for m and -3 for b.

Step 1: Identify the slope. Find the Negative Reciprocal. Problem B Step 2: Find the y-intercept Step 3: Write general y = mx + b equation Write an equation of the line that passes through the given point and is perpendicular to the given line. (4, 3), y = 4x - 7

Step 1: Identify the slope. Find the Negative Reciprocal. Problem B Step 2: Find the y-intercept Step 3: Write general y = mx + b equation Write an equation of the line that passes through the given point and is perpendicular to the given line. (4, 3), y = 4x - 7 ANSWER y = -(1/4)x + 4

Storm Check (Think, Write, Discuss, Report) How can you verify mathematically if two lines are perpendicular? I can verify that two lines are perpendicular when _______________________________________________ ______________________________________________.

Vocabulary Slope Parallel Lines Perpendicular Lines Slope-Intercept Form Point-Slope Form

Title: 6.5b Write Equations of Perpendicular Lines Date: Learning Target By the end of the period, I will write equations of perpendicular lines. 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 6.5 Pg. 357-359 3) Section ______ TxtBk.Prob.# 12,22,23,24,25,26 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

y = -2x – 5 y = -½x + 4 y = 2x – 3 y = ½x + 4 Ticket Out Multiple Choice Which line is perpendicular to the line y = -2x+4? Explain your answer. y = -2x – 5 y = -½x + 4 y = 2x – 3 y = ½x + 4 The two lines are perpendicular because ________________ __________________________________________________ _________________________________________________.

Their slopes are negative reciprocals. Ticket Out Multiple Choice Which line is parallel to the line y = -2x + 4 ? y = -2x – 5 y = -½x + 4 y = 2x – 3 y = ½x + 4 ANSWER C Their slopes are negative reciprocals.