## anonymous one year ago Determine the standard form of the equation of the line that passes through (9, -4) and (6, 4) Haaaaalp

1. misty1212

HI!!

2. anonymous

Hi!

3. misty1212

first we need the slope, because no matter what, if you want the equation of a line you need to have the slope do you know how to find ti?

4. anonymous

that would be -4+4 over 9+4 right?

5. misty1212

not quite

6. misty1212

you want to subtract, not add

7. anonymous

Oh, okay. Hold on Lemme try.

8. misty1212

kk

9. anonymous

ok so its -8/5 ??

10. misty1212

hmm $$9-6=?$$

11. anonymous

oh dang! I was doing -4. My bad. So it's 4.

12. misty1212

lets go slow

13. anonymous

Yes

14. misty1212

(9, -4) and (6, 4)

15. misty1212

first we do it the think way, then we do it the math teacher way

16. anonymous

Okay, it's like the third day of school. My brain doesn't work yet! sorry ahah.

17. misty1212

from 6 to 9 in the x is right 3 units from 4 to -4 in the y is down 8 units right 3, down 8 slope is $-\frac{8}{3}$

18. anonymous

okay, yes.

19. misty1212

now the math teacher way $\frac{y_2-y_1}{x_2-*x_1}=\frac{-4-4}{9-6}=-\frac{8}{3}$ or $\frac{4-(-4)}{6-9}=\frac{8}{-3}=-\frac{8}{3}$ either way

20. anonymous

okay, got it.

21. misty1212

who goes to school in the middle of august?

22. misty1212

ok no matter, now we have the the slope, and we can use the"point slope" formula because we have two points to choose form

23. anonymous

Everyone where I'm from starts in August. I know some places in California start later. so y=mx+b?

24. anonymous

wait, thats not right.

25. misty1212

no that is the "slope intercept " form we are not there yet

26. anonymous

y-y1 = m (x-x1)

27. misty1212

yeah that one

28. anonymous

Okay so -4 - 4 = -8/3 (9 - 6) ?

29. misty1212

ooh no

30. misty1212

the x and y in the formula are the variables you see in the answer only the $$x_1$$ and $$y_1$$ are numbers (as well as m )

31. misty1212

you put numbers everywhere

32. anonymous

oh. gosh ok. y+4= -8/3 (x-9)

33. misty1212

looks a lot better now

34. anonymous

subtracting a negative turns it into an addition basically, right?

35. misty1212

right

36. misty1212

now you should probably put it in "slope intercept" form aka solve for y

37. misty1212

you know how to do that? takes the same two steps every time

38. anonymous

Move the 4 to the other side?

39. misty1212

no not yet

40. misty1212

first distribute the $$-\frac{8}{3}$$ on the left

41. anonymous

oh yeah. so I multiply it or add it to the left?

42. misty1212

multiply

43. misty1212

$y+4=-\frac{8}{3}+24$ if my arithmetic is correct

44. misty1212

then don't "move the 4" subtract 4

45. misty1212

sorry, typo there i meant $y+4=-\frac{8}{3}x+24$ i dropped the x by mistake

46. anonymous

wait, where did 24 come? distributing the slope on the right side?

47. misty1212

yeah

48. misty1212

cancel the 3's

49. misty1212

$-\frac{8}{3}\times (-9)=3\times 8=24$

50. anonymous

Okay, I understand.

51. misty1212

so now we are at $y+4=-\frac{8}{3}x+24$ subtract 4 from both sides and you are done

52. anonymous

y=-8/3x+20

53. misty1212

yup

54. misty1212

took a while but i hope it is ok

55. anonymous

56. anonymous

Thanks by the way (:

57. misty1212

yeah it is the "final answer" as they say on tv you are quite welcome $\color\magenta\heartsuit$

58. anonymous

haha, of course! I'll give you a medal.

59. misty1212

thanks!