In Y=mx+b what is the formula to find b if you are given 2 points on a line???

Question

I have Y=-1/3x+b because i was given the points 5,4 and 2,5.... i just dont know the formula to find b from there....

Answer 1

If you're given two points on a line, you need to first get your slope, (m=(y1-y2)/(x1-x2)) which you've already done (and your answer is correct.)

You have two options from here:

Now, you can use the point-slope formula to get an equation for the line:
(y-y1)=m(x-x1)

Plug in the value of the slope which you found and solve for y. You will have to deal with some fractions.

Option 2: You know that y=-1/3x+b, and you have a couple of pairs of x and y points available to you. Pick an x and y and plug them into your formula and solve for b. You'll get the same answer this way (in fact, point-slope form is really just a generalization of what you did here).

Answer 2

Find first the slope: (yes, you already have that, but just in case :)

m = rise /run = (y2-y1) / (x2-x1)
--> doesn't really matter which point comes first as long as you're consistent, so:

m = (5-4) / (2-5)
m = -1/3

*You already have y = -1/3x + b

-- b is the y-intercept, the point where the line intersects the y-axis so that the x-value for b is 0, --> (0,b)

use your slope, one of your points (5,4) and (0,b) and substitute in your slope formula:

m = rise/run = (y2-y1) / (x2-x1)
-1/3 = (b-4) / (0-5)
5/3 + 4 = b
b = 5 2/3

or using the other point: (2,5)
-1/3 = (b-5) / (0-2)
2/3 + 5 = b
b = 5 2/3

Answer 3

y = mx + b (equation for a straight line).
y - mx = b (take the value of one of the points and put it in).
4 - m(5) = b (this is for point (5,4)).
4 - 5m = b
Now calculate the value of m. This is given by the difference of the y's divided by the difference of he x's.
Let point one be (5,4) and point two be (2,5).
m = [y2 - y1] / [x2 - x1]
m = [5 - 4] / [2 - 5]
m = -1/3
Now put this value into the equation.
4 - 5m = b
4 - 5(-1/3) = b
4 + 5/3 = b
b = 17/3
b = 5∙6666666666.............

Answer 4

First rearrange the formula to solve for b:

b = Y + (1/3)x

Plug in an x and y value from one point:

b = 4 + (1/3)(5)

b = 5 2/3 or 5.6666 or 17/3

Verify with other point

b = 5 +(1/3)(2)

b = 5 2/3

Answer 5

substitute in one of the given points for y and x

like
4=1/3(5)+b
or
5=1/3(2)+b

does that help?

Answer 6

b is the location where the line crosses the Y axis. So if you graph the two points and draw a line between them then "b" is where that line crosses the Y axis.

Answer 7

(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
now you rewrite in the form y=mx+b
(y-4)/(5-4)=(x-5)/(2-5)
(y-4)/1=(x-5)/-3
-3(y-4)=x-5
-3y+12=x-5
-3y=x-17
y=-1/3 x+17/3
b=17/3

Answer 8

b = y - 1/3x

Answer 9

Just use c and d, because they both come before e, which comes after b.