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# 1.3.1: 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 1.3.1: Creating and Graphing Linear Equations in Two Variables

2. 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. 3-4. Identify the slope and the y-intercept. slope _____ y-intercept ______ Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y- intercept. _____________ 1.3.1: Creating and Graphing Linear Equations in Two Variables

3. Equation: y = 2x + 2.50 Example 1, continued 6. Set up the coordinate plane and identify the independent and dependent variables. Graph the equation using the slope and y-intercept. Plot the y-intercept first and then use the slope to find the second point. 1.3.1: Creating and Graphing Linear Equations in Two Variables

4. 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: ___________________ 1.3.1: Creating and Graphing Linear Equations in Two Variables

5. Example 2, continued Use the y-intercept to help you graph your first point. Use the slope to help you find your second point. Vacuums sold 1.3.1: Creating and Graphing Linear Equations in Two Variables

6. 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. 3-4. Identify the slope and the y-intercept. slope _____ y-intercept ______ Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y- intercept. _____________ 1.3.1: Creating and Graphing Linear Equations in Two Variables

7. You Try , continued Use the y-intercept to help you graph your first point. Use the slope to help you find your second point. Hours 1.3.1: Creating and Graphing Linear Equations in Two Variables

8. 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: ___________________ 1.3.1: Creating and Graphing Linear Equations in Two Variables

9. Example 3, continued Graph the equation by making a table of values. 1.3.1: Creating and Graphing Linear Equations in Two Variables

10. 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: ___________________ 1.3.1: Creating and Graphing Linear Equations in Two Variables

11. Example 4, continued Graph the equation by making a table of values. 1.3.1: Creating and Graphing Linear Equations in Two Variables

12. 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. 3-4. Identify the slope and the y-intercept. slope _____ y-intercept ______ Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y- intercept. _____________ 1.3.1: Creating and Graphing Linear Equations in Two Variables

13. You Try, continued Graph the equation by making a table of values. 1.3.1: Creating and Graphing Linear Equations in Two Variables