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**4.5 Graphing Linear Equations**

A linear equation can be written in the form Ax + By = C. This is called the standard form of a linear equation. A ≥ 0, A and B are not both zero, and A, B, and C are integers whose greatest common factor is 1.

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**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. y = 5 – 2x y + 2x = 5 – 2x + 2x 2x + y = 5 The equation is now in standard form where A = 2, B = 1, and C = 5. This is a linear equation.

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**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. b. 2xy – 5y = 6 Since the term 2xy has two variables, the equation cannot be written in the form Ax + By = C. Therefore, this is not a linear equation.

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**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. c. 3x + 9y = 15 Since the GCF of 3, 9, and 15 is not 1, the equation is not written in standard form. Divide each side by the GCF. 3x + 9y = 15 3(x + 3y) = 15 x + 3y = 5 The equation is now in standard form where A = 1, B = 3, and C = 5.

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**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. d. 1/3 y = -1 To write the equation with integer coefficients, multiply each term by 3. 1/3 y = -1 3(1 /3 ) y = 3(-1) y = -3 The equation y = -3 can be written as 0x + y = -3. Therefore, it is a linear equation in standard form where A = 0, B = 1, and C = -3.

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**Graph Linear Equations**

The graph of a linear equation is a line. The line represents all the solutions of the linear equation. Also, every ordered pair on this line satisfies the equation.

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**Graph by Making a Table Graph x + 2y = 6.**

In order to find values for y more easily, solve the equation for y. x + 2y = 6 x + 2y – x = 6 – x 2y = 6 – x y = 3 – ½ x

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Graph by Making a Table

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Intercepts Since two points determine a line, a simple method of graphing a linear equation is to find the points where the graph crosses the x-axis and the y-axis. The x-coordinate of the point at which it crosses the x-axis is the x-intercept, and the y-coordinate of the point at which the graph crosses the y-axis is called the y-intercept.

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**Graph Using Intercepts**

Determine the x-intercept and y-intercept of 3x + 2y = 9. Then graph the equation. To find the x-intercept, let y = 0. 3x + 2y = 9 3x + 2(0) = 9 3x = 9 x = 3

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**Graph Using Intercepts**

Determine the x-intercept and y-intercept of 3x + 2y = 9. Then graph the equation. To find the y-intercept, let x = 0. 3x + 2y = 9 3(0) + 2y = 9 2y = 9 y = 4.5

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**Graph Using Intercepts**

The x-intercept is 3, so the graph intersects the x-axis at (3 , 0). The y-intercept is 4.5, so the graph intersects the y-axis is (0 , 4.5). Plot these points. Then draw a line that connects them.

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