10/1/15 Aim: Students will be able to determine if two lines are parallel or perpendicular. Homework: Textbook page 193 #’s 14-32 (Evens Only) Do Now:

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Presentation transcript:

10/1/15 Aim: Students will be able to determine if two lines are parallel or perpendicular. Homework: Textbook page 193 #’s (Evens Only) Do Now: Determine the slope of the line passing through the following pairs of points 1. (-1,-2) and (3,3) 2. (-2,3) and (1,-3) 3. (-4,-3) and (3,-3)

Quick Review/Preview 1. What is the Slope-Intercept Form? y = mx + b 2. What is the Standard Form? Ax + By = C 3. What is the Point-Slope Form? y – y 1 = m(x – x 1 ) 4. Find the “negative reciprocal” of each fraction

Overview Parallel Lines and Perpendicular Lines Property of their slopes Write equations for each type of lines

Parallel Lines Parallel Lines - lines that never intersect What is the slope of the red line? 1/2 What is the slope of the blue line? 1/2 Parallel Lines have the slope! same

Parallel Lines Determine if the lines are parallel 1. 2x + 6y = 12 6y = -2x + 12 yes

Parallel Lines Determine if the lines are parallel 2. 6x + 8y = -24 8y = -6x – 24 No

Parallel Lines Determine if the lines are parallel 3. 4x + 6y = -2 6y = -4x – 2 No

Equations of Parallel Lines 4. Write an equation for the line that contains (5, 1) and is parallel to m =

Equations of Parallel Lines 5. Write an equation for the line that contains (2, -6) and is parallel to m = 3 y + 6 = 3(x – 2)

Equations of Parallel Lines 6. Write an equation for the line that contains (-4, 3) and is parallel to m =

Perpendicular Lines Perpendicular Lines – lines that intersect to form right angles What is the slope of the red line? -1/4 What is the slope of the blue line? 4/1 Perpendicular Lines have slope! negative reciprocal

Perpendicular Lines What is the slope of the perpendicular line? 7. -5/2 8. 5/1 = /2

Equations of Perpendicular Lines 10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3 m =

Equations of Perpendicular Lines 11. Find the equation of the line that contains (1, 8) and is perpendicular to m =

Equations of Perpendicular Lines 12. Find the equation of the line that contains (2, -3) and is perpendicular to m = 2 y + 3 = 2(x – 2)

Perpendicular Lines 13. Determine if the lines are perpendicular: and No 14. Determine if the lines are perpendicular: and Yes

Determine whether AB and CD are parallel, perpendicular or neither for A(1,1), B(-1,-5), C(3,2) and D(6,1)

Challenge What is the slope of the line that is parallel to x = 4? undefined What is the slope of the line that is perpendicular to x = 4? zero

Wrap Up Parallel lines  Slopes  Determine if two lines are parallel  Write equations of parallel lines Perpendicular lines  Slopes  Determine slope of perpendicular lines  Write equations of perpendicular lines

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