## RealityWillSlapYou 2 years ago Select the equations that are parallel and perpendicular to y = −3x − 1 and that pass through the point (3, 1). A. parallel: y = −3x + 6 perpendicular: y = (1/3)x + 2(2/3) B. parallel: y = −3x + 10 perpendicular: y = (1/3)x C. parallel: y = -(1/3)x perpendicular: y = −3x D. parallel: y = (1/3)x + 1 perpendicular: y = 3x − 1

1. RealityWillSlapYou

@SmokeysTheName, Right here!

2. SmokeysTheName

ohhh man, remember i said i couldn't help? but here @phi might be able to

3. RealityWillSlapYou

Oh, oops! Sorry about that.... :)

4. SmokeysTheName

thats fine (:

5. SmokeysTheName

@hero can you help with this?

6. Hero

Pretty easy stuff @SmokeysTheName

7. SmokeysTheName

its been forever since ive done this and i can't remember /: so can you help him?

8. Hero

Hint: m1 x m2 = -1

9. RealityWillSlapYou

Umm.... I not really sure.. :|

10. Hero

m1 = -3 So m2 has to be a number such that when multiplied by m1, their product is -1.

11. RealityWillSlapYou

-1?

12. RealityWillSlapYou

Then 1 x -1 = -1

13. RealityWillSlapYou

Right?

14. Hero

m1 = -3 Multiply -3 by something to get -1

15. RealityWillSlapYou

I have no clue..... :|

16. SmokeysTheName

is that even possible @hero?

17. Hero

-3 x 1/3 = -1

18. Hero

Yes, it is possible.

19. Hero

So that's basically the slope of the second equation.

20. SmokeysTheName

oh yeah xD lol i dont like fractions so i didnt think of it. my bad okay ill stay out of this..

21. RealityWillSlapYou

Oh, why is math so hard for me to understand?!

22. Hero

So now, you have the slope and the point. Use the point slope formula to figure out the value of b.

23. RealityWillSlapYou

Y U NO WORK FOR ME MATH?! (ノಠ益ಠ)ノ

24. phi

sometimes it helps to watch these videos http://www.khanacademy.org/math/trigonometry/graphs/parallel_perpendicular/v/equations-of-parallel-and-perpendicular-lines

25. SmokeysTheName

phi is right, khan acad vids are great to watch

26. RealityWillSlapYou

@phi, in the video he was using two points and my question only has one point so how can I solve it the same way?

27. phi

at the very end he does a problem like yours.

28. RealityWillSlapYou

Oh, my video sever crashed after the second equation.

29. phi

but this video assumes you know about slopes and equations of lines (he has videos on all of that) for you problem, you should know that when you see y = mx +b m is the slope. the number multiplying the x is the slope

30. RealityWillSlapYou

I will start it back up again, but it will take 2 min.

31. RealityWillSlapYou

I tried to solve it (I think I did it wrong) and is it C?

32. phi

for you problem, you should know that when you see y = mx +b m is the slope. the number multiplying the x is the slope so what is the slope of your line y = −3x − 1 ?

33. RealityWillSlapYou

-3?

34. phi

do you see a number in front of the x ?

35. RealityWillSlapYou

So is the answer B?

36. phi

yes, -3 is the slope (that is why people came up with this kind of equation, you can read off the slope easily)

37. phi

from the video, you learned that parallel lines have what kind of slope ?

38. RealityWillSlapYou

The same slope

39. phi

look at your 4 choices. which choices have the correct slope of -3 for the parallel line ?

40. RealityWillSlapYou

Well it's A or B....... I think it's B

41. phi

no need to guess. now for the perpendicular line. Its slope is the negative inverse (or negative reciprocal) that means "flip" the slope and multiply by -1. For example if you had slope =2 $\frac{2}{1} ->- \frac{1}{2}$ can you do that for -3 ?

42. RealityWillSlapYou

$\frac{ 3 }{ 1 }?$

43. RealityWillSlapYou

Or$\frac{ 1 }{ 3 }?$

44. phi

3/1 is 3 start with -3 or -3/1 minus it : - -3/1 is +3/1 now flip it : 1/3 you know you did it right if it is the opposite sign of -3, and it's "upside down"

45. RealityWillSlapYou

Okay

46. phi

the slope of the perpendicular is 1/3 look at choices A or B. can we rule out either choice because it does not have 1/3 for the slope of the perpendicular line ?

47. RealityWillSlapYou

We can rule out A, right?

48. phi

for choice A, what is the number in front of the x for the perpendicular line ?

49. RealityWillSlapYou

-3

50. phi

that is the parallel line

51. phi

A. parallel: y = −3x + 6 perpendicular: y = (1/3)x + 2(2/3)

52. RealityWillSlapYou

So we rule out B?

53. phi

B. parallel: y = −3x + 10 perpendicular: y = (1/3)x what is the slope for the perpendicular line ?

54. RealityWillSlapYou

1/3

55. phi

so both A and B pass. we have to use the last bit of info pass through the point (3, 1) that says that when x=3 y must = 1 test choice B, perpendicular (because it looks the easiest) y = (1/3)x replace x with 3 and do the arithmetic what do you get ?

56. phi

replace x with 3 that means wherever you see an x, put a 3 in its place.

57. RealityWillSlapYou

okay give me a min.

58. RealityWillSlapYou

y = (1/3)3

59. RealityWillSlapYou

??

60. phi

yes, $y= \frac{1}{3} \cdot 3$ you can think of the 3 as 3/1 or $y= \frac{1}{3} \cdot \frac{3}{1}$ when you multiply fractions, multiply top times top and bottom times bottom you get $y= \frac{3}{3}$ can you simplify this ?

61. RealityWillSlapYou

y = 1

62. phi

so (3,1) is on this line. this is the choice

63. phi

if we put x=3 in choice A, we will not get y=1 btw, we should check the parallel line can you do that ? parallel: y = −3x + 10 what do you get if you replace x with 3

64. RealityWillSlapYou

-9

65. phi

what about the +10 ?

66. RealityWillSlapYou

1

67. phi

y = −3x + 10 if this does not give you y=1 when x=3 then it is not the line. But it does give y=1 so choice B. Does any of this make sense ?

68. RealityWillSlapYou

Yeah....

69. RealityWillSlapYou

How many more questions can you help me with?

70. phi

how many do you have ?

71. RealityWillSlapYou

Three, but I'm really bad at math.

72. phi

did you post them yet ?

73. RealityWillSlapYou

I posted one of them in algebra