1. Holt CA Course 1 2-7 Equations in Two Variables Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

2. Holt CA Course 1 2-7 Equations in Two Variables Warm Up Evaluate each expression for the given value of the variable. 1. 4x – 1 for x = 2 2. 7y + 3 for y = 5 3. x + 2 for x = –6 4. 8y – 3 for y = –2 7 38 –1 1 2 __ –19

3. Holt CA Course 1 2-7 Equations in Two Variables Preparation for AF1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results. California Standards

4. Holt CA Course 1 2-7 Equations in Two Variables Most movies shown in theaters are shot using film. The table shows the relationship between the duration of a movie in minutes and the length of the film in feet. Look for a pattern in the table. Duration of a Movie (min) Length of Film Needed (ft) 190 2180 3270 90(1) = 90 90(2) = 180 90(3) = 270

5. Holt CA Course 1 2-7 Equations in Two Variables The length of the film in feet is 90 times the duration of a movie in minutes. An equation in two variables can represent this relationship. Length in feetis90timesduration in minutes.

6. Holt CA Course 1 2-7 Equations in Two Variables Additional Example 1: Writing Equations from Tables x3456710 y1216202428 y is 4 times x. y = 4x Compare x and y to find a pattern. Use the pattern to write an equation. y = 4(10) Substitute 10 for x. y = 40 Use your equation to find y when x = 10. Write an equation in two variables that gives the values in the table. Use your equation to find the value of y for the indicated value of x.

7. Holt CA Course 1 2-7 Equations in Two Variables When all the y-values are greater than the corresponding x-values, try using addition or multiplication of a positive integer in your equation. Helpful Hint

8. Holt CA Course 1 2-7 Equations in Two Variables Check It Out! Example 1 x3456710 y56789 y is 2 more than x y = x + 2 Compare x and y to find a pattern. Use the pattern to write an equation. y = 10 + 2 Substitute 10 for x. y = 12 Use your equation to find y when x = 10. Write an equation in two variables that gives the values in the table. Use the equation to find the value of y for the indicated value of x.

9. Holt CA Course 1 2-7 Equations in Two Variables You can write equations in two variables for relationships that are described in words.

10. Holt CA Course 1 2-7 Equations in Two Variables Additional Example 2: Translating Words into Math The height of a painting is 7 times its width. h = height of painting Choose variables for the equation. h = 7w Write an equation. Write an equation for the relationship. Tell what each variable you use represents. w = width of painting

11. Holt CA Course 1 2-7 Equations in Two Variables Check It Out! Example 2 The height of a mirror is 4 times its width. h = height of mirror Choose variables for the equation. h = 4w Write an equation. Write an equation for the relationship. Tell what each variable you use represents. w = width of mirror

12. Holt CA Course 1 2-7 Equations in Two Variables The school choir tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $80 for 20 tickets, $88 for 22 tickets, and $108 for 27 tickets. Write an equation for the relationship. 1 Understand the Problem The answer will be an equation that describes the relationship between the number of tickets sold and the money received. Additional Example 3: Problem Solving Application

13. Holt CA Course 1 2-7 Equations in Two Variables You can make a table to display the data. 2 Make a Plan Solve 3 Let t be the number of tickets. Let m be the amount of money received. t202227 m8088108 m is equal to 4 times t. Compare t and m. m = 4t Write an equation.

14. Holt CA Course 1 2-7 Equations in Two Variables Substitute the t and m values in the table to check that they are solutions of the equation m = 4t. Look Back4 m = 4t (20, 80) 80 = 4 20 ? 80 = 80 ? m = 4t (22, 88) 88 = 4 22 ? 88 = 88 ? m = 4t (27, 108) 108 = 4 27 ? 108 = 108 ?

15. Holt CA Course 1 2-7 Equations in Two Variables The school theater tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $45 for 15 tickets, $63 for 21 tickets, and $90 for 30 tickets. Write an equation for the function. 1 Understand the Problem The answer will be an equation that describes the relationship between the number of tickets sold and the money received. Check It Out! Example 3

16. Holt CA Course 1 2-7 Equations in Two Variables You can make a table to display the data. 2 Make a Plan Solve 3 Let t be the number of tickets. Let m be the amount of money received. t152130 m456390 m is equal to 3 times t. Compare t and m. m = 3t Write an equation.

17. Holt CA Course 1 2-7 Equations in Two Variables Substitute the t and m values in the table to check that they are solutions of the equation m = 3t. Look Back4 m = 3t (15, 45) 45 = 3 15 ? 45 = 45 ? m = 3t (21, 63) 63 = 3 21 ? 63 = 63 ? m = 3t (30, 90) 90 = 3 30 ? 90 = 90 ?

18. Holt CA Course 1 2-7 Equations in Two Variables Lesson Quiz 1. Write an equation in two variables that gives the values in the table below. Use your equation to find the value for y for the indicated value of x. 2. Write an equation for the relationship. Tell what each variable you use represents. The height of a round can is 2 times its radius. h = 2r, where h is the height and r is the radius y = 3x; 21 x01357 y03915