Word Problems (In China!)

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Table of Contents Pg Title 26 Warm Up, Guided Practice 27 Writing Equations From Word Problems Notes

Warm-Up Write an equation in slope intercept form with the following information: Points: (-3, 2) and (4, 0) Points: (0, 6) and (0, -6)

Terracotta Army, Xi’an, China

Learning Intention/Success Criteria LI: We are learning to write linear equations from word problems. SC: I know how to 1. find the slope and points from a word problem 2. find the slope between two points 3. write linear equations in slope intercept form 4. analyze what m and b mean in context 5. solve equations for a variable

Revisited Vocabulary Slope A number which is used to indicate the steepness of a line Indicates if the line is tilted uphill or downhill Indicated by the letter “m” Point The pair of numbers giving the location on the coordinate plane Written in the form: (x, y)

Revisited Vocabulary Y-Intercept The point at which the function crosses the y-axis Indicated by the letter “b” Slope Intercept Form A way of writing an equation with a slope and y-intercept Written: f(x) = mx + b

Slope: Y-Intercept: Point(s): Example 1: Paul starts a small savings account to be used when he enters college. He starts off with a big initial deposit, plus $10 each month. After 13 months, Paul’s account has $430. Let n be the number of months since Paul starts the savings account and S(n) be the amount in the savings account after n months. Write an equation that describes this situation. Slope: Y-Intercept: Point(s): SC1 $10 Not provided (13, 430)

Example 1b: How big is Paul’s initial deposit? y = mx + b SC3 SC5 430 = (10)(13) + b 430 = 130 + b -130 -130 ___________________ 300 = b S(n) = 10n + 300 Example 1b: How big is Paul’s initial deposit? SC4 Paul’s initial deposit is $300

After 36 months, there will be $660 in the account Example 1c: How much money will Paul have in the account after 36 months? S(n) = 10n + 300 SC5 SC4 S(36) = 10n + 300 S(36) = 10(36) + 300 S(36) = 360 + 300 S(36) = 660 After 36 months, there will be $660 in the account

Guided Practice 1 Equation: Slope: Y-Intercept: Point(s): - 9 Zareen likes to stream online TV. The fee for this service is $9.00 a month. In January, she set aside money in a special account to pay for this service. She forgot how much she put into this special account initially, but she remembers that after 20 months, her special account will have $0.00. Write an equation that represents this situation where m is the number of months and A(m) is the amount of money left in the account. Equation: Slope: Y-Intercept: Point(s): - 9 y = -9x + 180 Not provided (20, 0)

Slope: Y-Intercept: Point(s): ?? ?? (600, 1400) (700, 1600) Example 2: The Academic T-Shirt Company did a cost study and found that it costs $1400 to produce 600 “I <3 Math” shirts. The total cost is $1600 to produce 700 shirts. Write an equation to represent this situation where s represents the number of shirts and C(s) represents the cost of producing these shirts. Slope: Y-Intercept: Point(s): ?? SC1 ?? (600, 1400) (700, 1600) m = y2 – y1 x2 – x1 SC2 SC3 m = 1600 – 1400 700 – 600 m = 200 100 m = 2

Slope: Y-Intercept: Point(s): m = 2 (600, 1400) (700, 1600) y = mx + b 1400 = (2)(600) + b 1400 = 1200 + b -1200 -1200 ___________________ 200 = b y = 2x + 200

This means that the start up fee to produce the shirts is $200. Example 2b: What is the y-intercept? What does it mean in context? y = 2x + 200 SC4 The y-intercept is 200. This means that the start up fee to produce the shirts is $200. The slope is 2. Example 2c: What is the slope? What does it mean in context? This means that each shirt costs $2 to produce.

Passport Stamp You’re looking at the Terracotta Army. How many army men are protecting you? The more protection you have, the more you understand the lesson.