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California Standards

California Standards. 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.

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California Standards

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  1. California Standards Preparation forAF1.0 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.

  2. 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. 90(1) = 90 90(2) = 180 90(3) = 270

  3. 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 feet is 90 times duration in minutes. x 90 y = .

  4. Compare x and y to find a pattern. Use the pattern to write an equation. Substitute 10 for x. Use your equation to find y when x = 10. Example 1: Writing Equations from Tables 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. y is 4 times x. y = 4x y = 4(10) y = 40

  5. Helpful Hint When all the y-values are greater than the corresponding x-values, try using addition or multiplication of a positive integer in your equation.

  6. You can write equations in two variables for relationships that are described in words.

  7. Choose variables for the equation. Write an equation. Example 2: Translating Words into Math Write an equation for the relationship. Tell what each variable you use represents. The height of a painting is 7 times its width. h = height of painting w = width of painting h = 7w

  8. 1 Understand the Problem Example 3: Problem Solving Application 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. The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

  9. 3 Solve Make a Plan 2 Compare t and m. Write an equation. You can make a table to display the data. Let t be the number of tickets. Let m be the amount of money received. m is equal to 4 times t. m = 4t

  10. Look Back ? ? ? ? 80= 4•20 88= 4•22 108= 4•27 108= 108 ? ? 80= 80 88= 88 4 Substitute the t and m values in the table to check that they are solutions of the equation m = 4t. m = 4t (20, 80) m = 4t (22, 88) m = 4t (27, 108)

  11. Compare x and y to find a pattern. Use the pattern to write an equation. Substitute 10 for x. Use your equation to find y when x = 10. Check It Out! Example 1 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. y is 2 more than x y = x + 2 y = 10+ 2 y = 12

  12. Choose variables for the equation. Write an equation. Check It Out! Example 2 Write an equation for the relationship. Tell what each variable you use represents. The height of a mirror is 4 times its width. h = height of mirror w = width of mirror h = 4w

  13. 1 Understand the Problem Check It Out! Example 3 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. The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

  14. 3 Solve Make a Plan 2 Compare t and m. Write an equation. You can make a table to display the data. Let t be the number of tickets. Let m be the amount of money received. m is equal to 3 times t. m = 3t

  15. Look Back ? ? ? 45= 3•15 63 = 3•21 90= 3•30 ? ? ? 45= 45 63= 63 90= 90 4 Substitute the t and m values in the table to check that they are solutions of the equation m = 3t. m = 3t (15, 45) m = 3t (21, 63) m = 3t (30, 90)

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