Building Equations Given Slope and a Point A-REI.3; F-LE.2; F-CED.2

Table of Contents 42: Guided Practice 43: How Do I Write Equations from Word Problems (Part 2)?

EQ: How Do I Write Equations From Word Problems? 11/20/2015

PointAlso known as an ordered pair Written (x, y) Slope Rise Run Change in y Change in x Rate of change Represented by “m”

Slope Formula Point – Slope Form y – y 1 = m(x – x 1 ) Slope – Intercept Form y = mx + b

Example 1a: Paul’s grandmother had started a small savings account for him to be used when he starts college. She started off with a big initial deposit, and then put in $10 every month after that. Paul asked his grandmother how much was in the savings account, and she told him that she started the account 13 months ago and that it currently has $430 in it. Let n be the number of months since Paul’s grandmother started the savings account and let S(n) be the amount in the savings account after n months. Slope: $10 Y - Intercept: ?? Point 1: (13, 430) Equation: y – 430 = 10(x – 13) Point 2: ??

Example 1b: How big was Paul’s grandmother’s initial deposit? y – 430 = 10(x – 13) y – 430 = 10x – ________________ y = 10x Paul’s grandmother’s initial deposit was $300.

Example 1c: How much money will Paul have in the account after 3 years (36 months)? y = 10x y = 10(36) y = y = 660

Guided Practice Kanoa likes to watch movies and TV shows streaming online. The fee for this service is $9 per month. At the beginning of the year, he set aside a bunch of money in a special account to pay for his streaming movie service. He forgot how much he put into this special account initially, but he remembers that after 20 months, his special account will have $0. Write an equation that represents this situation. Slope:Y-Intercept: Point 1:Point 2: Equation: -9 ?? (20, 0) y – 0 = -9(x – 20) ??

Guided Practice 1 Follow Up 1 What is the slope – intercept form of the equation? y – 0 = -9(x – 20) y = -9(x – 20) y = -9x + 180

Guided Practice 1 Follow Up 2 How much money did Kanoa have in his account to begin with? $180

Questions What is the break even point and how do you find it? How do you know if you should use slope-intercept form or point slope form? What information can you get from slope-intercept form that you can’t get from point-slope form?

Example 2a: Mahalo Middle School rented a movie theater for a 7 th grade field trip. The theatre charges an initial fee for reserving the facility for a private showing, and then charges a fee for each person in attendance. When the school initially called the theatre, 120 students and teachers were going to attend. The quote they got for this number was $710. At the last minute, however, more students turned in their forms. For the actual field trip 144 students and teachers attended, costing the school $812. Slope: ?? Y - Intercept: ?? Point 1: (120, 710) Equation: ?? Point 2: (144, 812)

(120, 710) (144, 812) m = y 2 – y 1 x 2 – x 1 m = 812 – – 120 m = m = 4.25

y = mx + b 710 = (4.25)(120) + b 710 = b -510 _______________ 200 = b y = 4.25x + 200

Example 2b: What is the y- intercept and what does it mean in context? The y-intercept is 200. It means that Mahalo Middle School must pay $200 regardless of the number of students that go on the trip.

Example 2c: What is the slope and what does it mean in context? The slope is 4.25 The slope means that for every student that goes on the trip, the cost raises $4.25

Guided Practice 2 The Masiks need to drain their swimming pool in order to repair a leak. For this project, they decide to rent a pump to remove the water. The graph provided represents the number of gallons of water remaining in their pool as the function of the number of minutes the pump is used. Notice that this graph indicates that after 35 minutes of running the pump, 8880 gallons of water remained in the pool. After 125 minutes, 6000 gallons remained. **Page 14** Slope:Y-Intercept: Point 1:Point 2: Equation: ?? (35, 8880) ?? (125, 6000)

m = y 2 – y 1 x 2 – x 1 m = – 125 Guided Practice 2 m = m = -32 y – 8880 = -32(x – 35) y – 8880 = -32x __________________ y = -32x + 10,000

Guided Practice 2 Follow Up 1 What is the y-intercept and what does it mean in context? The y-intercept is 10,000 This means that the pool initially has 10,000 gallons of water in it

Guided Practice 2 Follow Up 2 After how many minutes will the pool be out of water? The pool will be empty after minutes.

Questions After finding the slope, is it easier to use the point-slope form or the slope- intercept form? Why? Where is the break even point on a graph? What does the y-intercept tell you? What does the slope tell you?

Classwork/Homework For classwork/homework, please do pages 35 – 38. When finished, rip/cut them out and turn them in.