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5.5 parallel and_perpendicular_lines

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5.5 parallel and_perpendicular_lines

1. 1. Slope, Parallel and Perpendicular Lines SWBAT verbally tell me how the slope of parallel lines and perpendicular lines are related. They can find the equation of a line parallel/perpendicular to a given line that passes through a given point.
2. 2. Try these…..Review 1.Find the reciprocal of each fraction a. b. c. d. 2.Find the slope and y-intercept of each equation 2 1 3 4 3 1 − 2 5 − 26d.6c.8 3 5 b.4 4 5 a. +==−=+= xyxyxyxy
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 – y1 = m(x – x1) 4. Find the “negative reciprocal” of each fraction 3 4 d. 2 1 c. 7 3 b. 5 2 a. −− 4 3 2 1 2 3 7 2 5 =−−
4. 4. Overview  How to calculate a slope  Parallel Lines and Perpendicular Lines  Write equations for each type of lines
5. 5. Notes Finding the Slope of a Line Slope is found using the equation m= y2 -y1. x2 -x1 The coordinates for the points on the graph are plugged into the equation above. The equation is then solved and the remaining solution is the slope. Example: Let (x1, y1) = (-3, 5) and (x2, y2) = (2, 1)
6. 6. Notes Classifying Lines Using Slope  A line with a positive slope rises from left to right. (m>0)  A line with a negative slope falls from left to right. (m<0)  A line with a slope of zero is horizontal. (m=0)  A line with an undefined slope is vertical. (m is undefined.) Positive Slope Negative Slope Zero Slope Undefined Slope
7. 7. Notes Continued Slopes of Parallel and Perpendicular Lines Parallel Lines The lines are parallel if and only if they have the same slope. m1 = m2 Perpendicular Lines The lines are perpendicular if and only if their slopes are negative reciprocals of each other m1 = - 1 or m1m2 = -1 m2 Parallel Lines Perpendicular Lines
8. 8. 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
9. 9. Parallel Lines Determine if the lines are parallel 1. 2x + 6y = 12 6y = -2x + 12 yes 5 3 1 and1262 +−==+ xyyx 2 3 1 +−= xy
10. 10. Parallel Lines Determine if the lines are parallel 2. 6x + 8y = -24 8y = -6x – 24 No 3 4 3 and2486 −=−=+ xyyx 3 4 3 +−= xy
11. 11. Parallel Lines Determine if the lines are parallel 3. 4x + 6y = -2 6y = -4x – 2 No 8 3 2 and264 −=−=+ xyyx 3 1 3 2 −−= xy
12. 12. 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
13. 13. Perpendicular Lines What is the slope of the perpendicular line? 7. -5/2 8. 5/1 = 5 9. 1/2 8 5 2 −= xy xy 5 1 −= 72 −−= xy
14. 14. Equations of Perpendicular Lines 10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3 m = 5 1 − xy 5 1 2 −=+
15. 15. Equations of Perpendicular Lines 11. Find the equation of the line that contains (1, 8) and is perpendicular to m = 1 4 3 += xy 3 4 − ( )1 3 4 8 −−=− xy
16. 16. 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) 6 2 1 +−= xy
17. 17. Perpendicular Lines 13. Determine if the lines are perpendicular: and No 14. Determine if the lines are perpendicular: and Yes 4231 3 2 =++= xyxy 9345 3 4 =+−= xyxy 423 =+ xy 423 +−= xy 3 4 3 2 +−= xy 934 =+ xy 934 +−= xy 4 9 4 3 +−= xy
18. 18. 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