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**Graphing Using Intercepts**

4.3 Graphing Using Intercepts 1. Given an equation, find the coordinates of the x- and y-intercepts. 2. Graph linear equations using intercepts.

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**Standard Form of a Linear Equation in 2-Variables**

A, B and C are integers. A ≥ 0 No fractions! A can’t be negative.

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**Is the given equation written in standard form? If not, rewrite it.**

No, A can’t be negative. 4x - 3y = -7 No, can’t have fractions. 2x + 3y = 6 Yes. No, x term must be written first. 5x – 2y = -3 A: Yes B: No

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**Given an equation, find the coordinates of the x- and y-intercepts.**

Objective 1 Given an equation, find the coordinates of the x- and y-intercepts. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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**The point where the graph crosses an axis is called an intercept.**

The point where a graph intersects the x-axis is called the x-intercept. (4, 0) intersects the y-axis is called the y-intercept. (0, -2) x-intercept (4, 0) y-intercept (0, 2) What do you notice about the intercepts?

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**To find an x-intercept:**

To find a y-intercept: 1. Let y = 0. 1. Let x = 0. 2. Solve for x. 2. Solve for y.

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**Find the x- and y-intercepts for 7x – 2y = 14**

Example 1 Find the x- and y-intercepts for 7x – 2y = 14 x-intercept: let y = 0 7x – 2y = 14 7x – 2(0) = 14 7x = 14 x = 2 x-intercept: (2, 0) y-intercept: let x = 0 7x – 2y = 14 7(0) – 2y = 14 –2y = 14 y = –7 y-intercept: (0, –7) Always write an ordered pair!

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**Find the x- and y-intercepts for**

Example 2 Find the x- and y-intercepts for x-intercept: let y = 0 3x + 2(0) =18 3x = 18 x = 6 x-intercept: (6, 0) y-intercept: let x = 0 3(0) + 2y = 18 2y = 18 y = 9 y-intercept: (0, 9)

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**Find the x- and y-intercepts for**

Example 3 Find the x- and y-intercepts for x-intercept: let y = 0 y-intercept: let x = 0

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**Find the x- and y-intercepts for**

Example 4 Find the x- and y-intercepts for x-intercept: let y = 0 y-intercept: let x = 0 0 = 6 Not true. Horizontal line. No x-intercept. 0x + y = 6 y = 6 (0, 6)

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**Find the x- and y-intercepts for**

Example 5 Find the x- and y-intercepts for x-intercept: let y = 0 y-intercept: let x = 0 x + 0y = -4 x = -4 (-4, 0) 0 = -4 Not true. Vertical line. No y-intercept.

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Objective 2 Graph linear equations using intercepts.

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**Graph: 7x – 2y = 14 From Example 1: x-intercept: (2, 0)**

y-intercept: (0, -7) 7x – 2y = 14

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Example 7 Graph: x-intercept: (-4, 0) y-intercept: (0, 8)

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**Graph: x-intercept: y-intercept: Need another point.**

Example 8 Graph: x-intercept: (0, 0) y-intercept: Need another point. Choose a value for x or y and solve. (5, -4)

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**Graph: Example 9 Equation has only a y.**

Line intersects only the y-axis. Horizontal line through -3.

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**What is the x-intercept for 3x – y = 6?**

b) (0, –6) c) (–6, 0) d) (0, 2) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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**What is the x-intercept for 3x – y = 6?**

b) (0, –6) c) (–6, 0) d) (0, 2) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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**What is the y-intercept for y = 2x – 6?**

b) (0, –6) c) (–6, 0) d) (0, 3) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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**What is the y-intercept for y = 2x – 6?**

b) (0, –6) c) (–6, 0) d) (0, 3) Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.

Graph a linear equation Graph: 2x – 3y = -12 Solve for y so the equation looks like y = mx + b - 3y = -2x – 12 Subtract 2x to both sides. y = x + 4 Divide.

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