Name ______________________________ Date___________ #9 Chapter #____5_____Assignment Section #___5.6b_____Page Number___330‐335_____ Section Title: Parallel and Perpendicular Lines
Assignment: Worksheet Notes Complete Assignment Complete Teacher Signature/Date:
____________________
Target Goals: The students will be able to: 

determine whether lines are parallel, perpendicular, or neither.
write equations of parallel and perpendicular lines.
NOTES/OPENER:
1‐4 1. Look back through your notes, if you need, to complete
the following. Fill in the blanks. If the _____________ of the two lines are opposite reciprocals of each other, then the lines are ______________________. 2. If two lines have the __________ ___________, then they are parallel. 3. The opposite reciprocal of 
4. 2
The opposite reciprocal of is ___________. 7
5. 7
is ___________. 11
Classify each pair of equations as representing lines that are parallel, perpendicular, or neither. (Hint: Solve each for y to determine the slope.) a. 7 x  5 y  12
14 x  10 y  27
b. 12 x  6 y  24
x  2 y  13
6. Write the equation of the line, in standard form, parallel to the graph of the given equation and passing through the given point. 2 x  5 y  3,  2, -3 7. Write the equation of the line, in standard form, perpendicular to the graph of the given equation and passing through the given point. More Opener/Notes 5 x  y  2, (2, 3) 8. Suppose y varies directly with x, and y = 49 when x = ‐7.  Find k.  What direct variation equation relates x and y?  Find the value of y when x = 13. 9. Suppose y varies directly with x, and y = 5 when x = 25.  Find k.  What direct variation equation relates x and y?  Find the value of y when x = ‐40. 10‐11 Graph each direct variation equation. Be sure to name 2 points on each line and use a straight edge. 5
11. y = x 10. y = ‐3x 7
ASSIGNMENT‐‐#9 Worksheet
When you are done with assignment #9 and you have gone on line to grade the
assignment, with a RED pen, assess your learning!!
Target Goal: The students will be able to:
 determine whether lines are parallel, perpendicular, or neither.
 write equations of parallel and perpendicular lines.
Get it _________Needs more Practice________Need extra help_______
#9‐‐Chapter Five Section 5.6b Worksheet Show all work and circle your solutions. 1‐11 Mixed Review 1. Find the slope of the line passing through (7, ‐9) and (‐5, ‐1). 2. Find the slope of the line passing through (‐6, 8) and (‐6, 22). 3. The equation of a vertical line through (‐6, ‐7) is: 4. Find the x‐intercept and y‐intercept of the line whose equation is 12x – 13y = 26. 5. Find the x‐intercept and y‐intercept of the line whose equation is 5x – 4y = ‐20. 6. Find the slope of the line whose equation is 15x – 5y = 45. 7. Write the equation of a horizontal line which passes through the point (23,‐23). 8. Write the equation of a vertical line which passes through the point (23, ‐23). 9. Write the equation in standard form: y ‐ 5 = ‐6(x + 8) 3
10. Write the equation in standard form: y + 5 =  (x ‐ 9) 8
11. Graph the line 3x – 4y = ‐24 12‐17 Write an equation of the line, in standard form, that passes through the given point and is parallel to the graph of the given equation. 12. (3, 2); 3x ‐ y = 2 14. (‐8, 6); x + 4y = 20 13. (4, 1); ‐2x + y = 14 15. (6,2); y  2 x  19 3
16. (10, 5); y  3 x  7 17. (3, 4); y = 2 2
____________________________________________________________________________ 18‐23 Determine whether the graphs of the given equations are parallel, perpendicular, or neither. Explain. 18. y = 4x + 5 19. y = 6x  8 x + 6y = 12 4x + y = 13 7
7
21. y = 20. y = x – 7 9
8
7
y =  x + 3 x = ‐4 9
22. y = 4x + 12 23. 3x + 6y = 12 1
x + 4y = 32 y – 4 =  (x + 2) 2
____________________________________________________________________________ 24‐26 Determine whether each statement is always, sometimes, or never true. Explain. 24. Two lines with different slopes are perpendicular. 25. The slopes of vertical lines and horizontal lines are negative reciprocals. 26. A vertical line is perpendicular to the x‐axis. 27‐32 Write an equation of the line, in standard form, that passes through the given point and is perpendicular to the graph of the given equation. 27. (2, 1); 2x + y = 1 1
28. (7, 5); y = x + 2 3
30. (9, 3); 3x + y = 5 29. (3, 6); x + y = 4 2
32. (0, 5); x  6y = 2 31. (8, 3); y+4 =  (x  2) 3
____________________________________________________________________________ 33. What is the slope of a line that is parallel to the x‐axis? 34. What is the slope of a line that is perpendicular to the x‐axis? 35. What is the slope of a line that is parallel to the y‐axis? 36. What is the slope of a line that is perpendicular to the y‐axis? ____________________________________________________________________________ 37‐40 Mixed Review 37. Find the slope of the line whose equation is 4 x  5 y  10 . 3
38. If line f has a slope of  , then what is the slope of a line perpendicular to f? 8
39. Determine the slope and y‐intercept for the line with the equation: 5 x  7 y  14 . 40. Determine the x‐ and y‐intercepts for the line with the equation: 5 x  3 y  30 . 41‐42 PUTTING IT ALL TOGETHER  a) Find the slope of the line passing through each pair of points. b) Write the equation of the line in point/slope form. (y – y1) = m(x – x1) c) Write the equation in slope‐intercept form. y = mx + b d) Write the equation in standard form. Ax + By = C e) Find the x‐ and y‐intercepts of the line. f) Graph each line. (Name 2 points and use a straight edge.) 41. (7, ‐1) and (‐2, 5) 42. (3, ‐3) and (4, 8) m = ________ m = ________ pt/slope_____________ pt/slope_____________ slp/int_____________ slp/int _____________ Standard_____________ Standard_____________ x‐int_____________ x‐int _____________ y‐int_____________ y‐int _____________ graph graph