## pau08 3 years ago please answer this: How will you determine the equation of the line if the given are two points of the line? i really need the answer... thank you

1. ChrisV

first find the slope, m=(y2-y1)/(x2-x1)

2. ChrisV

then write it in slope intercept form y-y1=m(x-x1)

3. Directrix

What if I make up two points and work the problem I made up? Will that help?

4. pau08

okey....

5. Directrix

Points ( 2, -1 ) and ( -4, -5 ) lie on a line. Find the equation of the line that contains then. Leave your answer in y = mx + b form.

6. Directrix

First, get the slope. Think of slope as change in y over change in x. m designates the slope of a line and has formula [y2 - y1] / x2 - x 1 ] . The y2 is not y^2 but what we call y sub 2 because the 2 is a subscript which is hard to type.

7. Directrix

One of our points will be (x1, y1) and the other (x2, y2) It does not matter which is which.

8. Directrix

Let (x1,y1) be (2, -1) and let (x2, y2) be (-4, -5) Questions so far?

9. pau08

what is y=mx+b

10. Directrix

That is the form we will leave the equation of our line in. So, if we get something like 2x + 7y = 2/3, then that's not y = mx+b form.

11. pau08

ah okey

12. Directrix

You don't have to leave the equation in that form unless instructed to do so. Most books do request that or standard form.

13. Directrix

Focus on cranking out this slope right now.

14. pau08

okey

15. Directrix

|dw:1329213587734:dw|

16. Directrix

4/6 = 2/3 so the slope m is 2/3. Note the use of grouping symbols to help prevent sign problems or "sinus" problems as I call them. :)

17. Directrix

Do you follow how the slope came to be 2/3?

18. pau08

ah okey

19. pau08

yes

20. pau08

you simplify it

21. pau08

|dw:1329268007717:dw|

22. Directrix

Yes.

23. Directrix

Hey, I like "okey." I understand it means "yes."

24. Directrix

Okey, now we use the point slope formula to get the equation of the line.

25. Directrix

y - y1 = m (x - x1) y - y1 = (2/3) ( x - x1)

26. pau08

okey can i solve it?

27. Directrix

(x1,y1) be (2, -1) from above. y - (-1) = (2/3) ( x - 2)

28. pau08

oh, i change my mind i don't want to answer it

29. Directrix

We're almost finished. I'll finish if you have to go.

30. pau08

i'll have to go now eh... can we finish it now??

31. Directrix

y - (-1) = (2/3) ( x - 2) y + 1 = 2/3 (x - 2) multiply both sides by 3 3(y + 1) = (3) (2/3) (x-2)

32. Directrix

3y +3 = 2 (x-2) 3y + 3 = 2x - 4

33. pau08

transpose it, right?

34. Directrix

Yes, thought you left, :) 3y = 2x - 7

35. pau08

36. pau08

37. Directrix

y = (2/3) x - 7/3 in y = mx + b form where m is the slope and (-7/3) is the y-intercept.

38. Directrix

Look at the cool graph: http://www.wolframalpha.com/input/?i=line+%282%2C-1%29+and+%28-4%2C-5%29+

39. Directrix

One last word. There is no quick and short way to learn math but once you do learn it, you will be proud of yourself.

40. Directrix

Just takes practice like anything else. :)

41. pau08

42. Directrix

y = (2/3) x - 7/3

43. pau08

ah...........T.Y.P

44. Directrix