## anonymous one year ago I have a question about the slope.... In the slope formula y=mx+b what is the difference between the y and the b and how do I know when to plug it in to the y or b?

1. Nnesha

b is y-intercept a point where line cross y-axis(there would be only one ) y = just y-coordinate you don't need to plug anything for y

2. anonymous

Example problem: Line A has slope of -5/3 and passes through the point (-2,7). WHat is the x-intercept of line A?

3. Nnesha

yes y=mx+b so replace m with -5/3 y=-5/3x+b now you have x y value (-2,7) x=-2 y=7 substitute x and y for their solve for b(y-intercept )

4. anonymous

I just don't understand what to plug into the y or b.... like if they ask it passes through the line then what do i do? use it for the y or b?

5. Nnesha

x-intercept is a point where line cross the x-axis when y =0 after you find y-intercept substitute y for 0

6. anonymous

Like what are some examples of when i have to use it for y or b? what do they have to say for me to know where to replace it?

7. Nnesha

when they say passes through the points (x,y) then you have to find b

8. anonymous

so replace the b with the number they say it passes through the points?

9. anonymous

or the y

10. Nnesha

replace with y not b (b is y-intercept )

11. anonymous

hmmm okay

12. Nnesha

here is an example slope =2 passes through (4,3) $\huge\rm \color{reD}{y}=mx+b$$(4,\color{ReD}{3})$

13. anonymous

So in what cases do i replace the b (y-intercept) what kind of problems do they have to ask for

14. Nnesha

then statement would be like this slope is 3 and ***Y-INTERCEPT =5

15. Nnesha

they would use the *y-intercept ) word

16. anonymous

hmmm okay

17. phi

maybe this helps??: y = 3x + 2 is a formula to "find y" if you are told x. you then put the x and y together as a package (x,y) for example, if x is 1, y will be 5 (do you see how?) and (1,5) is the "package" which is just a way to say the point (1,5) is on the line. does that part make any sense?

18. phi

the next idea is we can (in theory) find all the points on the line using its formula that can be useful and the reason we want a formula rather than a long boring list of (x,y) pairs

19. anonymous

hmmmm i mean thats easy i'm just hving a hard time understand when to substitute the y or b

20. Nnesha

|dw:1439238885626:dw| i know why you r confused but y-intercept is the specific point where line cross the y-axis which is also one of the y value but they will always use the y-intercept word for b

21. phi

you will get the idea... but I want to make sure you got the basic idea the next idea is how do we find the formula for a line? it turns out you need just two points on the line, and there is a way to do that.

22. anonymous

what if they don't specifically use the term y-intercept like how will i know to plug what in where?

23. phi

as you know, the formula for a line is y= m x + b where m is the slope and b is the "y-intercept" if you are given two points, they you know how to find the slope, right ?

24. anonymous

2 points like (5, 2)? yea then just plug in 5 to x and 2 to b right?

25. Nnesha

when they say given points where (3,5) where first number represent x-coordinate and and 2nd number represent the y-coordinate (NOT y-intercept )

26. Nnesha

y-coordinate =y y-intercept = b

27. phi

**2 points like (5, 2)? *** oooh! no! a point is (x,y) pair. (5,2) is one point. to find it, you go over 5 and up 2 to get to it.

28. phi

two points would be for example (1,3) and (4,4)

29. anonymous

so then 3=m(1)+b?

30. phi

yes, you can do that. but the first step is to find m (which we can do) change in y divided by change in x what do you get for m ?

31. anonymous

y2-y1/x2-x1

32. phi

yes, and for (1,3) and (4,4) what do you get for m?

33. anonymous

1/3

34. phi

ok. now we go back to the equation 3=m(1)+b and put in m= 1/3 3= 1/3 * 1 + b or 3= 1/3 + b sorry about the ugly numbers... but we can solve for b by adding -1/3 to both sides.

35. phi

you get b= 3 - 1/3 or 8/3 notice if we start with y = 1/3 x + b and put in the other point (4,4) 4 = 1/3 * 4 + b 4= 4/3 + b 4- 4/3 = b and b= 12/3 - 4/3 = 8/3 we get the same b

36. anonymous

yea i know about that u'll always get the same solution no matter which u plug in

37. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @yomamabf 2 points like (5, 2)? yea then just plug in 5 to x and 2 to b right? $$\color{blue}{\text{End of Quote}}$$ also when the statement is *passes through point * that means solve for b easy way to memorize it ;)

38. phi

if you are given two points, you find the equation of the line by 1) find the slope 2) use either (x,y) pair to replace the x and y in the equation with numbers and solve for b does that sound ok?

39. phi

if you are told the y-intercept is 3 (for example) that is the same info as telling you that (0,3) is a point on the line (y-intercept is the y value when x is 0)

40. anonymous

hmmm okay got it

41. phi

say the problem was: slope is 3 y intercept is 3 what is the equation? two ways to do it: y = mx + b we are told m is 3, so y= 3x + b (0,3) is a point on the line 3= 3*0 + b 3 = b so y= 3x+3 the other way: replace m with 3 (the slope), and replace b with 3 (the y-intercept) y = 3x+3

42. anonymous

yea i was thinking the latter

43. phi

yes, but it is good to see how to do it the first way. It always helps to see problems solved in different ways.

44. anonymous

hmmm okay got it

45. anonymous

thank you!!!!

46. phi

the first way is how you do it for any point on the line. (0,3) is just an easy point (because it tells us what b is ... or multiplying x by 0 is easy)

47. anonymous

okay i'm going to try to find another problem and see if i can do it by myself i need practice =(

48. phi

if you get lost, post the problem