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- 1. Slope, Parallel and Perpendicular Lines .
- 2. Try these…..Review 1.Find the reciprocal of each fraction a. 1 2 b. 4 3 c. 1 − 3 d. 5 − 2 2.Find the slope and y-intercept of each equation 5 a. y = x + 4 4 5 b. y = x − 8 3 c. y = 6 x d. y = 6 x + 2
- 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 2 3 7 1 2 4 3 5 a. b. − c. − − = 2 d. − 5 7 3 2 1 3 4 2
- 4. Overview How to calculate a slope Parallel Lines and Perpendicular Lines Write equations for each type of lines
- 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. 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. 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. 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 same slope!
- 9. Parallel Lines Determine if the lines are parallel 1 1. 2 x + 6 y = 12 and y = − x + 5 3 2x + 6y = 12 6y = -2x + 12 1 y = − x+2 3 yes
- 10. Parallel Lines Determine if the lines are parallel 3 2. 6 x + 8 y = −24 and y = x − 3 4 6x + 8y = -24 8y = -6x – 24 3 y = − x +3 4 No
- 11. Parallel Lines Determine if the lines are parallel 2 3. 4 x + 6 y = −2 and y = x −8 3 4x + 6y = -2 6y = -4x – 2 2 1 y = − x− 3 3 No
- 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 negative reciprocal slope!
- 13. Perpendicular Lines What is the slope of the perpendicular line? 2 7. y = x − 8 5 1 8. y = − x 5 9. y = −2 x − 7 -5/2 5/1 = 5 1/2
- 14. Equations of Perpendicular Lines 10. Find the equation of the line that contains (0, -2) and is perpendicular to y = 5x + 3 1 m=− 5 1 y+2=− x 5
- 15. Equations of Perpendicular Lines 11. Find the equation of the line that contains (1, 8) and is perpendicular to 3 y = x+1 4 4 m =− 3 4 y − 8 = − ( x − 1) 3
- 16. Equations of Perpendicular Lines 12. Find the equation of the line that contains (2, -3) and is perpendicular to 1 y = − x+ 6 2 m=2 y + 3 = 2(x – 2)
- 17. Perpendicular Lines 13. Determine if the lines are perpendicular: 2 y = x + 1 and 3 y + 2 x = 4 3 3y + 2x = 4 3 y = −2 x + 4 2 4 y =− x+ 3 3 No 14. Determine if the lines are perpendicular: 4 y = x − 5 and 4 y + 3 x = 9 3 4y + 3 x = 9 4 y = −3 x + 9 y =− 3 9 x+ 4 4 Yes
- 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

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