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GRAPHING LINEAR EQUATIONS Linear Equations • Independent variable (x): the quantity that changes based on values you choose • Dependent variable (y): the quantity that is based on the input values of the independent variable Warm Up Steps for creating linear equations: 1. Read the problem. 2. Determine the known quantities. 3. Identify the slope and the y-intercept. 4. Substitute the slope and y-intercept into the equation y=mx+b. 5. Graph the equation. 1. A local convenience store owner spent $10 on pencils to resell at the store. What is the equation that store’s revenue if each pencil sells for $0.50? Graph the equation using a table of values. 2. A taxi company in Atlanta charges $2.50 per ride plus $2 for every mile driven. Write and graph the equation (using the slope and y-intercept) that models this scenario. 3. Miranda gets paid $300 a week to deliver groceries. She also earns 5% commission on any orders she collects while out on her delivery run. Write an equation that represents her weekly pay and then graph the equation. 4. A Boeing 747 starts out a long flight with about 57,260 gallons of fuel in its tank. The airplane uses an average of 5 gallons of fuel per mile. Write an equation that models the amount of fuel in the tank then graph the equation using a graphing calculator. 5. You can buy a 6-hour phone card for $5, but the fine print says that each minute you talk actually costs you 1.5 amount of time. What is the equation that models the number of minute left on the card compared with the number of minutes you actually talked? What is the graph of this equation? Warm Up One form of the element beryllium, beryllium-11, has a half-life of about 14 seconds and decays to the element boron. A chemist starts out with 128 grams of beryllium-11. She monitors the element for 70 seconds. 1. What is the equation that models the amount of beryllium-11 over time? 2. How many grams of beryllium-11 does the chemist have left after 70 seconds? GRAPHING EXPONENTIAL EQUATIONS Exponential Equations Review • General form: • Growth: the base is greater than 1 • Decay: the base is between 0 and 1 Compound Interest • A: initial value • P: principle amount • r: interest rate • n: number of years Compound Interest Cheat Sheet Compounded… n (number of times per year) Year/annually 1 Semi-annually 2 Quarterly 4 Monthly 12 Weekly 52 Daily 365 1. If a pendulum swings to 90% of its height on each swing and starts out at a height of 60 cm, what is the equation that models this scenario? What is its graph? 2. The bacteria Streptococcus lactis doubles every 26 minutes in milk. If a container of milk contains 4 bacteria, write an equation that models this scenario and then graph the equation. 3. An investment of $500 is compounded monthly rate of 3%. What is the equation that models this situation? Graph the equation. Warm Up