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**Day Problems Graph each equation.**

1. y – 2 = (x – 3) 2. y + 3 = -2(x – 1) Write an equation in point-slope form for the line through the given point with the given slope. 3. (4 , 2); m = (-5 , 2); m = 0 A line passes through the given points. Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form. 5. (-1 , 0) , (1 , 2)

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**6.5 Parallel and Perpendicular Lines 2/22/11**

Parallel lines – lines in the same plane that never intersect.

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**Slopes of Parallel Lines**

Nonvertical lines are parallel if they have the SAME SLOPE and DIFFERENT Y-INTERCEPTS. Any two vertical lines are parallel. Example – The equations y = 2x + 1 and y = 2x + 3 have the same slope, 2, and different y-intercepts. The graphs of the two equations are parallel.

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**Determining Whether Lines are Parallel**

Are the graphs of and 2x + 6y = 12 parallel? Explain. Write 2x + 6y = 12 in slope-intercept form. Then compare with The lines are parallel. The equations have the same slope, , and different y-intercepts.

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**Writing Equations of Parallel Lines**

Write an equation for the line that contains (5 , 1) and is parallel to Step 1 – Identify the slope of the given line. Step 2 – Write an equation of the line through (5 , 1) using point-slope form, then change to slope-intercept.

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**Perpendicular Lines 2/23/11**

Perpendicular lines – lines that intersect to form right angles. SLOPES OF PERPENDICULAR LINES Two lines are perpendicular their slope is the opposite reciprocal of the given slope. A vertical and horizontal line are also perpendicular. EXAMPLE – the slope of is The slope of y = 4x + 2 is 4.

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**Opposite Reciprocal How to find the opposite reciprocal of a number:**

Start with Find its Write the a fraction reciprocal opp. reciprocal Start with Find its Write its an integer reciprocal opp. reciprocal

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**Writing Equations for Perpendicular Lines**

Find an equation of the line that contains (0 , -2) and is perpendicular to y = 5x + 3. Step 1- Identify the slope of the given line. m = 5 Step 2 – Find the opposite reciprocal of the slope: Step 3 – Use the slope-intercept form to write an equation.

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**More Practice!!! Textbook – p. 314 #2 – 30 even.**

Homework – Worksheet 6.5.

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