1. anonymous

The equation of line AB is y=-1/6x-1. Write and equation of a line perpendicular to line AB in slope-intercept form that contains point(-4,3)(Hint:y-y1=M(x-x1)

2. jdoe0001

what's the slope of line AB?

3. anonymous

idk that is everything that came with the equation

4. jdoe0001

http://4.bp.blogspot.com/-2hRw4bmioCw/Ut8B2Kcq_8I/AAAAAAAAAi4/dRwSEZQdAHw/s1600/Slope-Intercept+Form.gif <--- notice the example, notice the slope so... what do you think would be the slope of AB then?

5. anonymous

is it -7

6. jdoe0001

ahemmm... check the picture, or your book, on the slope-intercept form since that's what y=-1/6x-1 is in

7. anonymous

no this is an example on a lesson online I don't get it

8. freckles

The slope of line AB is given since the line AB is given. You can find the answer to which @jdoe0001 seeks by comparing your line y=-1/6*x-1 to y=m*x+b. y=m*x+b is called slope-intercept form because it tells you the slope m and the y-intercept b.

9. anonymous

so is x -4/3

10. freckles

not entirely sure what you are answering just now but I was asking for the slope of y=-1/6*x-1 notice this is in slope-intercept form it tells you the slope and the y-intercept all you have to do is compare y=-1/6*x-1 to y=m*x+b can you identify the slope m (compare the two lines) ?

11. anonymous

y=-4*x+3 <------is this it

12. freckles

y=-1/6*x-1 upon comparing this to y=m*x+b you should see m=-1/6 the slope of line AB (y=-1/6*x-1) is -1/6 -- now to find the slope of the perpendicular line just solve the following $\text{ Solve the following for } m_1 \text{ which I'm going to call the slope } \\ \text{ of the perpendicular line } \\ m \cdot m_1=-1 \\ \text{ where we found } m=\frac{-1}{6} \\ \frac{-1}{6} \cdot m_1=-1$ --- one you have found that your perpendicular line in point-slope form will be: $y-y_1=m_1(x-x_1) \\ \text{ where you are given } (x_1,y_1) \text{ as } (-4,3)$

13. anonymous

m1=-7 correct

14. freckles

how did you get -7?

15. anonymous

-4-3

16. freckles

did you try solving the equation I gave at all?

17. freckles

you want to isolate m_1 try multiplying both sides by what it is being divided by try multiplying both sides by -6

18. anonymous

yeah I was trying to figure what m1 was so i could multiply by -1/6

19. freckles

instead of solving that equation you could also ask yourself what is the opposite reciprocal of -1/6

20. freckles

opposite means: The opposite of a is -a The opposite of -a is a. You just take the number and change the sign to find the opposite. reciprocal means (if it exists) : The reciprocal of a is 1/a. The reciprocal of 1/a is a. You just take the number and flip it. So if I say find the opposite reciprocal of -1/6, this means you will change sign and also flip.

21. anonymous

multiply -4 and 3 by 6

22. anonymous

you know what I'll give you a medal for helping, but clearly this is not going through to my head so I will just guess

23. freckles

I know you can find the opposite reciprocal of -1/6... Just change the sign and then flip.

24. freckles

Changing the sign... it is negative, make it positive 1/6 now flip it, 6/1 or also known as 6. The slope of the perpendicular line is 6. You could have also solved that equation I gave. $\frac{-1}{6} m_1=-1 \\ \text{ multiply both sides by -6 } \\ (-6) \frac{-1}{6} m_1=(-6)(-1) \\ \text{ notice } \frac{6}{6}=1 \\ (- \cancel{6})\frac{-1}{\cancel{6}}m _1=(-6)(-1) \\ \text{ also recall } (-)(-)=+ \\ +m_1=+(6)(1) \\ \text{ so we have } m_1=6$

25. anonymous

m1=6 is the equation of a line perpendicular to line AB in slope-intercept

26. freckles

no

27. freckles

that is just the slope of the perpendicular line

28. freckles

I gave the perpendicular line in point-slope form above all you have to do is plug in numbers into it

29. anonymous

oh wait so is it -4/3*6=-1

30. freckles

no I don't know where you got that from but -4/3*6 isn't -1 isn't -24/3 which is -8

31. anonymous

where did you get those numbers from

32. freckles

I think you are looking for what I typed above where I gave you the point slope form of the perpendicular line which was: $y-y_1=m_1(x-x_1) \\ \text{ where you are given } (x_1,y_1) \text{ as } (-4,3)$

33. anonymous

the question I posted says to use those numbers Write and equation of a line perpendicular to line AB in slope-intercept form that contains point(-4,3)

34. freckles

once you enter in the numbers above like you found m_1 and you are given x_1 and y_1 you can write in slope-intercept form which is y=slope*x+(y-intercept) y=m_1*x+b

35. anonymous

so it is y=m_1*-4-3

36. freckles

you found m_1 to be 6 replace m_1 with 6 you are given x_1 as -4 replace x_1 with -4 you are given y_1 as 3 replace y_1 with 3

37. anonymous

so the answer after solving equation is -42

38. freckles

no you are suppose to get an equation

39. freckles

I will give the equation in point-slope form one more time $y-y_1=m_1(x-x_1)$

40. freckles

replace m_1 with 6 replace x_1 with -4 replace y_1 with 3

41. anonymous

so its y-3=6(x+4)

42. freckles

yes now just put in slope-intercept form

43. freckles

distribute and add 3 on both sides

44. freckles

have to go peace

45. anonymous

46. freckles

no y-3=6(x+4) is a line you cannot go from a line to just a numerical value like 42 slope-intercept is of the form y=mx+b just use distributive property on 6(x+4) then add the 3 on both sides

47. anonymous

@freckles 3*6+4*3

48. freckles

do you know the distribute property? if you have a(b+c) then distributive property says this is a*b+a*c

49. freckles

50. anonymous

I thought I knew what it meant so is it 6*x+4*x @freckles

51. freckles

6(x+4) by distributive property we can rewrite this as 6*x+6*4 or 6x+24 so you have y-3=6(x+4) y-3=6x+24 now add 3 on both sides y=6x+24+3 y=6x+27

52. freckles

this is of the form y=mx+b which we call slope-intercept form

53. freckles

y=6x+27 is a line that is perpendicular to y=-1/6x-1 and also goes through the point (-4,3)

54. anonymous

@freckles thank you so much no one gave me such a clear response as you and helped me get it. thank you again

55. freckles

Well hopefully this will be a good example on how to do other similar problems.

56. freckles

Way to hang in there. I know math can be tough but you can get it with practice and more practice.