Lesson 2.6 Creating and Graphing Linear Equations in Two Variables
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1 Lesson 2.6 Creating and Graphing Linear Equations in Two Variables Concept: Graphing Linear Equations EQ: How do I create and graph a linear equation in two variables from a word problem? (Standard CED.2) Vocabulary: Slope, Y-Intercept, Independent & Dependent Variable 1
2 Creating & Graphing Linear Equations 1. Read the problem statement carefully. 2. Look for the information given and make a list or underline the known quantities. 3. Determine which information tells you the rate of change, or the slope, m. Look for words such as each, every, per, or rate. 4. Determine which information tells you the y-intercept, or b. This could be an initial or starting value, a flat fee, and so forth. 5. Substitute the slope and y-intercept into the linear equation formula, y = mx + b. 6. Set up the coordinate plane and identify the independent and dependent variables. 7. Graph the equation by using the slope and y-intercept or by making a table of values. 2
3 Guided Practice - Example 1 A taxi company in Atlanta charges $2.50 for a ride plus $2 for every mile driven. Write and graph the equation that models the taxi company s total fees. 1. Read the problem. 2. Determine the known quantities Identify the slope and the y-intercept. slope y-intercept 5. Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y- intercept. 3
4 Example 1, continued 6. Set up the coordinate plane and identify the independent and dependent variables. 7. Graph the equation using the slope and y- intercept. Plot the y- intercept first and then use the slope to find the second point. Equation: y = 2x
5 Guided Practice - Example 2 Matthew receives a base weekly salary of $300 plus commission of $50 for each vacuum he sells. Write and graph the equation that models his weekly earnings. Slope: y-intercept: Equation: 5
6 Example 2, continued y = 50x Use the y-intercept to help you graph your first point. Use the slope to help you find your second point. Vacuums sold 6
7 You Try! A 12-inch candle burns at a rate of 2 inches per hour. Write and graph the equation that models the height of the candle over time. 1. Read the problem. 2. Determine the known quantities Identify the slope and the y-intercept. slope y-intercept 5. Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y- intercept. 7
8 You Try, continued y = 2x + 12 Use the y-intercept to help you graph your first point. Use the slope to help you find your second point. Hours 8
9 Guided Practice - Example 3 A water company charges a monthly fee of $6.70 plus a usage fee of $2.60 per 1,000 gallons used. Write and graph the equation that models the water company s total fees. Slope: y-intercept: Equation: 9
10 Example 3, continued y = 2. 6x Graph the equation by making a table of values. x y
11 Guided Practice - Example 4 A local convenience store owner spent $10 on pencils to resell at the store. Write and graph the equation of the store s revenue if each pencil sells for $0.50. Slope: y-intercept: Equation: 11
12 Example 4, continued y = 1 2 x 10 Graph the equation by making a table of values. x y
13 You Try! Maddie borrowed $1,250 from a friend to buy a new TV. Her friend doesn t charge any interest, and Maddie makes $40 payments each month. Write and graph the equation that models the money Maddie owes. 1. Read the problem. 2. Determine the known quantities Identify the slope and the y-intercept. slope y-intercept 5. Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y- intercept. 13
14 You Try, continued y = 40x Graph the equation by making a table of values. x 0 6 y 21 14
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