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**Warm Up Find the slope of the line containing each pair of points.**

1. (0, 2) and (3, 4) (–2, 8) and (4, 2) 3. (3, 3) and (12, –15) Write the following equations in slope-intercept form. 4. y – 5 = 3(x + 2) 5. 3x + 4y + 20 = 0

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Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

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In lesson 5-6 you saw that if you know the slope of a line and the y-intercept, you can graph the line. You can also graph a line if you know its slope and any point on the line.

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**Example 1A: Using Slope and a Point to Graph**

Graph the line with the given slope that contains the given point. slope = 2; (3, 1)

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**Example 1B: Using Slope and a Point to Graph**

Graph the line with the given slope that contains the given point. slope = ; (–2, 4)

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**Example 1C: Using Slope and a Point to Graph**

Graph the line with the given slope that contains the given point. slope = 0; (4, –3)

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Check It Out! Example 1 Graph the line with slope –1 that contains (2, –2).

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**Substitute into the slope formula.**

If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1). Let (x, y) be any other point on the line. Substitute into the slope formula. Slope formula Multiply both sides by (x – 2). 3(x – 2) = y – 1 Simplify. y – 1 = 3(x – 2)

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**Example 2: Writing Linear Equations in Point-Slope Form**

Write an equation in point-slope form for the line with the given slope that contains the given point. A. B. C.

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Check It Out! Example 2 Write an equation in point-slope form for the line with the given slope that contains the given point. a. b. slope = 0; (3, –4)

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**Example 3: Writing Linear Equations in Slope-Intercept Form**

Write an equation in slope-intercept form for the line with slope 3 that contains (–1, 4). Step 1 Write the equation in point-slope form: Step 2 Write the equation in slope-intercept form by solving for y.

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Check It Out! Example 3 Write an equation in slope-intercept form for the line with slope that contains (–3, 1). Add 1 to both sides.

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**Check It Out! Example 3 Continued**

Write an equation in slope-intercept form for the line with slope that contains (–3, 1).

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**Example 4A: Using Two Points to Write an Equation**

Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1)

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Example 4A Continued Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1)

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**Example 4B: Using Two Points to Write an Equation**

Write an equation in slope-intercept form for the line through the two points. (0, 1) and (–2, 9)

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Example 4B Continued Write an equation in slope-intercept form for the line through the two points. (0, 1) and (–2, 9)

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Check It Out! Example 4a Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10)

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**Check It Out! Example 4a Continued**

Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10)

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Check It Out! Example 4b Write an equation in slope-intercept form for the line through the two points. (6, 3) and (0, –1)

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**Check It Out! Example 4b Continued**

Write an equation in slope-intercept form for the line through the two points. (6, 3) and (0, –1)

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**Example 5: Problem-Solving Application**

The cost to stain a deck is a linear function of the deck’s area. The cost to stain 100, 250, 400 square feet are shown in the table. Write an equation in slope-intercept form that represents the function. Then find the cost to stain a deck whose area is 75 square feet.

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Check It Out! Example 5 What if…? At a newspaper the costs to place an ad for one week are shown. Write an equation in slope-intercept form that represents this linear function. Then find the cost of an ad that is 21 lines long.

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Lesson Quiz: Part I Write an equation in slope-intercept form for the line with the given slope that contains the given point. 1. Slope = –1; (0, 9) 2. Slope = ; (3, –6) Write an equation in slope-intercept form for the line through the two points. 3. (–1, 7) and (2, 1) 4. (0, 4) and (–7, 2)

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Lesson Quiz: Part II 5. The cost to take a taxi from the airport is a linear function of the distance driven. The cost for 5, 10, and 20 miles are shown in the table. Write an equation in slope-intercept form that represents the function.

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