Solving Word Problems by Writing Equations in Slope-Intercept Form MS Algebra A-F-IF-7 – Ch. 6.1c Solving Word Problems by Writing Equations in Slope-Intercept Form Mr. Deyo Solving Word Problems by Writing Equations in Slope-Intercept Form A 3,000 lb. mass is approaching your head at 40 ft/sec.

Title: 6.1c Solve Word Problems with the Slope-Intercept Form Date: Learning Target By the end of the period, I will solve word problems by writing and solving equations in slope-intercept form. 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 6.1 Pg. 327-328 3) Section ______ TxtBk.Prob. #42,43,44,45,47,49 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

A 3,000 lb. mass is approaching your head at 40 ft/sec. 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 A 3,000 lb. mass is approaching your head at 40 ft/sec.

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

Daily Warm-Up Exercises For use with pages xxx–xxx Bill borrowed $75 from his parents. He is paying back $5 per week. Write an equation that models this situation.

Daily Warm-Up Exercises For use with pages xxx–xxx Bill borrowed $75 from his parents. He is paying back $5 per week. Write an equation that models this situation. ANSWER y = 75 – 5x  y = -5x + 75

Slope-Intercept Form of a Linear Equation How To Get To Slope-Intercept Form 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 = mx + b Solve for b (Y1) = m(X1) + b Step 3) Write general formula with m and b y = mx + b m = slope b = y-intercept Slope-Intercept Form of a Linear Equation

Problem A RECORDING STUDIO Solve a multi-step problem A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour. Write an equation that gives the total cost of an album as a function of studio time (in hours). Find the total cost of recording an album that takes 10 hours of studio time. C = total cost T = number of hours m = $35 per hour b = $50 initial cost y = mx + b

C = $400 C = 35T + 50 Problem A ANSWER RECORDING STUDIO Solve a multi-step problem A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour. Write an equation that gives the total cost of an album as a function of studio time (in hours). Find the total cost of recording an album that takes 10 hours of studio time. C = total cost T = number of hours m = $35 per hour b = $50 initial cost y = mx + b C = 35T + 50 C = 35(10) + 50 C = 350 + 50 C = $400 C = 35T + 50 y = mx + b

Problem B WHAT IF? In Problem A, suppose the recording studio raises its initial fee to $75 and charges $40 per hour for studio time. Write an equation that gives the total cost of an album as a function of studio time (in hours). Find the total cost of recording an album that takes 10 hours of studio time.

Problem B ANSWER WHAT IF? In Problem A, suppose the recording studio raises its initial fee to $75 and charges $40 per hour for studio time. Write an equation that gives the total cost of an album as a function of studio time (in hours). Find the total cost of recording an album that takes 10 hours of studio time. y = mx + b C = 40T + 75 C = 40(10) + 75 C = 400 + 75 C = $475 C = 40T + 75

Vocabulary Check y-intercept slope slope-intercept form standard form conditional statement parallel In the equation y = mx + b, the value of m is the _____________ of the graph of the equation. In the equation y = mx + b, the value of b is the _____________ of the graph of the equation. 3. Two lines are _________________ if their slopes are equal.

parallel Vocabulary Check slope y-intercept y-intercept slope slope-intercept form standard form conditional statement parallel ANSWER slope In the equation y = mx + b, the value of m is the _____________ of the graph of the equation. ANSWER y-intercept In the equation y = mx + b, the value of b is the _____________ of the graph of the equation. ANSWER parallel 3. Two lines are _________________ if their slopes are equal.

(4, 5) and (2, 3) (0, 0) and (-1, 2) Skills Check #1 Find the slope of the line that passes through the points. (4, 5) and (2, 3) (0, 0) and (-1, 2)

Skills Check #1 Find the slope of the line that passes through the points. (4, 5) and (2, 3) (0, 0) and (-1, 2) ANSWER ANSWER 3-5 2-4 -2 2 -1 = = 2-0 -1-0 1 = = -2

6 – 4 3 x = y 5 2 = y – x Skills Check #2 Identify the slope (m) and y-intercept (b) of the line with the given equation. 6 – 4 3 x = y 5 2 = y – x

Skills Check #2 Identify the slope (m) and y-intercept (b) of the line with the given equation. 6 – 4 3 x = y 5 2 = y – x ANSWER ANSWER 4 3 5 -2 m = , b = –6 m = , b = –2

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

Title: 6.1c Solve Word Problems with the Slope-Intercept Form Date: Learning Target By the end of the period, I will solve word problems by writing and solving equations in slope-intercept form. 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 6.1 Pg. 327-328 3) Section ______ TxtBk.Prob. #42,43,44,45,47,49 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

Ticket OUT. Find the slope or y-intercept given a point Find the value of m or b if the given line passes through the given point. y = 2x + b (8, -4) Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you.

Ticket OUT. Find the slope or y-intercept given a point SOLUTION Find the value of m or b if the given line passes through the given point. y = 2x + b (8, -4) mx b + = y Substitute the coordinates of the given point into the equation and solve for b. -4 = 2(8) + b Turn to your partner and share your answer. Please use correct answer. Partner B, please share what Partner A told you. -4 = 16 + b -20 = b