how do you get the y intercept in y=mx+b?

Question

like if the points are (1.5,1) and (3,2)

Answer 1

equation is (y-1)/1=(x-1.5)/1.5
3/2y-3/2=x-3/2
3y=2x
y=3/2x
y intercept is 0

Answer 2

points take the form (x, y), so substitute x = 1.5, y = 1 and x = 3, y = 2 into y = mx + b to get a simultaneous system of two linear equations in the two unknowns m and b:

1 = (1.5)x + b
2 = 3x + b

from this, you can eliminate x:

2 = 3x + 2b (obtained by multiplying the first equation by 2)
2 = 3x + b

subtracting 2nd equation from the 1st, one gets:

(2b - b) + (3x - 3x) = b = 2 - 2 = 0

hence, the y-intercept is b = 0.

(by the way, I forgot to mention that from an equation y = mx + b for a specific line, m is the slope and b is the y-intercept.)

Answer 3

The y intercept is where your straight line crosses the y-axis. The y-axis could be more infomatively referred to as the x=0 axis since everywhere along the y-axis x=0. So, if you plug in x=0 into your equation, you have:

y = (m x 0) + b = b.

The y-intercept is therefore just given by b.


Oh I see, if you have two actual points then just go:

y1 = m * x1 +b
y2 = m* x2 + b

Subtract equation 2 from equation 1:

y1-y2=m(x1-x2)

divide this equation by (x1-x2) (as long as x2 and x1 are not the same number of course):

m = (y1-y2)/(x1-x2)

Now plug this into one of the first two equations above:

b = y - [(y1-y2)/(x1-x2)]*x

where y and x can be given by either one of the two points.

So yes the y-intercept is exactly zero. So why am I answering this since that's what everyone got already?

Answer 4

In the equation "y=mx+b" the y-intercept is "b".
The y-intercept for the given points is as follows...

y2-y1
x2-x1
=slope

2-1 = 1
3-1.5 = 1.5

1/1.5 = slope (m)
1/1.5 = 2/3

(y-y1)=m(x-x1)

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

In this case the 2's cancelled out.
So your equation is "y=2/3x"
There is no "b" shown, but there is an invisible "b". So your y-intercept is "0"... or the origin.

Your welcome
Always,
Vicki

Answer 5

you have to find the equation of the line first and to find that equation,
you have to find the slope

slope = (y2-y1)/(x2-x1) = (2-1)/(3-1.5) = 1/1.5 = 2/3

so now we have y=(2/3)x+b

pick 1 of the 2 points you are given and plug the x and y in

2=(2/3)(3) + b
2=2+b
b=0

y=(2/3)x so the y intercept is 0

Answer 6

The point-slope equation of a line is

y-y1=m(x-x1)

y=mx+b
If your linear equation is written in this form, m represents the slope and b represents the y-intercept.

Answer 7

The value of b is the y intercept.

Think of it this way, set x = 0 (definintion of the y intercept) and all you have left is y = b

Ken

Answer 8

its b in the equation and its 0

Answer 9

first u find y1-y2/x1-x2 the plug the solution in m in the y=mx+b.
but put it like this (y-y1)=m(x-x2)
use 1.5,1 and plug like this (y-1)=m(x-1.5)

Answer 10

plot it and do the line. that's the hard way, i forgot how to put it into the other equation...