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Published byKelley Barnett Modified over 7 years ago

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**Warm-Up 5 minutes 1. Graph the line y = 3x + 4.**

3. What is the slope of the lines in the equations above?

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**Parallel and Perpendicular Lines**

Objectives: To determine whether the graphs of two equations are parallel To determine whether the graphs of two equations are perpendicular

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Parallel Lines Parallel lines are lines in the same plane that never intersect. Parallel lines have the same slope. -8 -6 -4 -2 2 4 6 8

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**Example 1 Determine whether these lines are parallel. y = 4x -6 and**

The slope of both lines is 4. So, the lines are parallel.

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**Example 2 Determine whether these lines are parallel. y – 2 = 5x + 4**

and -15x + 3y = 9 +15x x y = 5x + 6 3y = x y = 3 + 5x y = 5x + 3 The lines have the same slope. So they are parallel.

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**Example 3 Determine whether these lines are parallel. y = -4x + 2 and**

+2y y 2y - 5 = 8x 2y = 8x + 5 Since these lines have different slopes, they are not parallel.

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**Practice Determine whether the graphs are parallel lines.**

1) y = -5x – 8 and y = 5x + 2 2) 3x – y = -5 and 5y – 15x = 10 3) 4y = -12x + 16 and y = 3x + 4

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Example 4 Write the slope-intercept form of the equation of the line passing through the point (1, –6) and parallel to the line y = -5x + 3. slope of new line = -5 y – y1 = m(x – x1) y – (-6) = -5(x – 1) y + 6 = -5x + 5 y = -5x - 1

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Practice Write the slope-intercept form of the equation of the line passing through the point (0,2) and parallel to the line 3y – x = 0.

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Practice 2 Determine whether the graphs of the equations are parallel lines. 3x – 4 = y and y – 3x = 8 2) y = -4x + 2 and -5 = -2y + 8x

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Perpendicular Lines Perpendicular lines are lines that intersect to form a 900 angle. -8 -6 -4 -2 2 4 6 8 The product of the slopes of perpendicular lines is -1.

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**Example 1 Determine whether these lines are perpendicular. and**

y = -3x - 2 m = -3 Since the product of the slopes is -1, the lines are perpendicular.

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**Example 2 Determine whether these lines are perpendicular. y = 5x + 7**

and y = -5x - 2 m = -5 Since the product of the slopes is not -1, the lines are not perpendicular.

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**Practice Determine whether these lines are perpendicular.**

1) 2y – x = 2 and y = -2x + 4 2) 4y = 3x and -3x + 4y – 2 = 0

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Example 3 Write an equation for the line containing (-3,-5) and perpendicular to the line y = 2x + 1. First, we need the slope of the line y = 2x + 1. m = 2 Second, we need to find out the slope of the line that is perpendicular to y = 2x + 1. Lastly, we use the point-slope formula to find our equation.

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Practice Write an equation for the line containing the given point and perpendicular to the given line. 1) (0,0); y = 2x + 4 2) (-1,-3); x + 2y = 8

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