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Tables and Functions #42

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VOCABULARY A function is a rule that relates two quantities so that each input value corresponds exactly to one output value.

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**Example 1: Writing Equations from Function Tables**

Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x. 16 13 10 7 4 y 3 2 1 x

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Example 2 Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x. 18 15 12 9 y 10 6 5 4 3 x ?

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Example 3 Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x. 17 15 13 11 y 8 7 6 5 x ?

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**You can write equations for functions that are described in words.**

VIP You can write equations for functions that are described in words.

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**Example 4: Translating Words into Math**

Write an equation for the function. Tell what each variable you use represents. The height of a painting is 7 times its width.

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Example 5 Write an equation for the function. Tell what each variable you use represents. The height of a mirror is 4 times its width.

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Example 6 Write an equation for the function. Tell what each variable you use represents. A large pie costs $2 more than a small pie.

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**Example 7: 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 function.

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Example 8 The school band tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $60 for 20 tickets, $66 for 22 tickets, and $81 for 27 tickets. Write an equation for the function.

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**Example 9: Finding Solutions of Equations with Two Variables**

Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4.

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Example 10 Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4.

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FYI Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.

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**Example 11: Checking Solutions of Equations with Two Variables**

Determine whether the ordered pair is a solution to the given equation. (3, 21); y = 7x

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Example 12 Determine whether the ordered pair is a solution to the given equation. (6, 4); y = 2x - 7

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VOCABULARY You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.

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**Example 13: Reading Solutions on Graphs**

Use the graph of the linear function to find the value of y for the given value of x. x = 4 x y 4 2 -2 -4

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Example 14 For each graph of a linear function, find the values of y for the values of x given below the graph. x = 0 y 2 x 9 8 7 6 5 1 3 4 10

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Example 15 For each graph of a linear function, find the values of y for the values of x given below the graph. x = 4 y 2 x 9 8 7 6 5 1 3 4 10

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**Example 16: Graphing Linear Functions**

Graph the function described by the equation. y = 3x+ 2

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Example 17 Graph the function described by the equation. y = 8 - x

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