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?

- anonymous

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- 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

- 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?

- 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 )

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## More answers

- 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?

- Nnesha

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

- 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?

- Nnesha

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

- anonymous

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

- anonymous

or the y

- Nnesha

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

- anonymous

hmmm okay

- Nnesha

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

- anonymous

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

- Nnesha

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

- Nnesha

they would use the *y-intercept ) word

- anonymous

hmmm okay

- 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?

- 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

- anonymous

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

- 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

- 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.

- anonymous

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

- 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 ?

- anonymous

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

- 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 )

- Nnesha

y-coordinate =y
y-intercept = b

- 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.

- phi

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

- anonymous

so then 3=m(1)+b?

- 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 ?

- anonymous

y2-y1/x2-x1

- phi

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

- anonymous

1/3

- 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.

- 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

- anonymous

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

- 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 ;)

- 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?

- 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)

- anonymous

hmmm okay got it

- 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

- anonymous

yea i was thinking the latter

- 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.

- anonymous

hmmm okay got it

- anonymous

thank you!!!!

- 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)

- anonymous

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

- phi

if you get lost, post the problem

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