y = mx + b, right? So how do you get the numbers to write this? What do all those letters mean?

Remember that m is the slope and b is the y-intercept. Slope is simply “rise over run”. On a graph, you can sit and count the rise and then the run to get the slope, but how do you find it if all you have is two points?

How about m = (y2 – y1)/(x2 -x1). You have two points so you have two x and two y. Just pick one point to be the y1 and x1 and the other to be y2 and x2; it doesn’t matter which, as long as you stay consistant. I’m going to put (6,3) as y2 and x2. Remember that a point is (X,Y).

So m = (3 – 1)/(6 – 2) = 2/4. Leave in fraction form, but you can (and probably should unless told otherwise by your teacher simplfy). So 2/4 = 1/2

Ok so now you have m, but you don’t have b. How do you find b?

B is the y-intercept, or the point at which the line crosses the y-axis (that’s the vertical one). You now have m, and you have two points to pick from for the y and x, so can’t you just solve for b?

I’m going to use (2,1).

So: y = mx + b

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

1 = 1 + b

-1 -1

0 = b

remember for multiplying fractions, 2 is the same as 2/1 and then you just multiply across. so (1 x 2)/(2 x 1) = 2/2 = 1

So now you know m and b, so you can write your equation.

y = (1/2)x

because b = 0, you can just not write it in the equation (or you could write y = (1/2)x + 0.

Now pick a point and plug it in to check your work.

3 = (1/2)(6)

(1 x 6)/(2 x 1)

6/2

3

3 = 3 so your equation is correct.

y = mx + b

where,

m = slope

b = y-intercept

First, find slope, m:

Use this equation:

m = (y2 – y1) / (x2 – x1)

x1 is 2 from point (2,1)

y2 is 1 from point (2,1)

x2 is 6 from point (6,3)

y2 is 3 from point (6,3)

Plug these points in the slope equation:

m = [(3) – (1)] / [(6) – (2)]

m = 2/4 = 1/2

Back to the original equation:

y = mx + b

plug in 1/2 in m:

y = (1/2)x + b

To find b, plug in any of the two points you were given, (2,1) or (6,3). I recommend using the point that’s easiest to calculate, which is (2,1):

y = (1/2) x + b

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

Then find b:

1 = 1 + b

0 = b

Plug that b back in the original equation:

y = 1/2x + b

y = 1/2x + 0

Since b is 0, you don’t have to show b:

y = 1/2x

And you end up with the above equation for the line (2,1) and (6,3).

y=mx +b

This is called the slope-intercept form because “m” is the slope and “b” gives the y-intercept.

Start off with finding the slope by using the slope equation.

Subtract the second y point with the 1st y point and do the same with the X.

3-1

—-=

6-2

2

— or

4

1/2.

So the slope is 1/2. Then you plugin the slope and one of the points (2,1) or (6,3). ( it does matter which point, because you will end up with the same answer)

1=1/2(2)+ b

1=1+b

b= 0

So your equation would be

y=1/2X (because 1/2x +0=1/2x

y=mx+b or (y-y’)=m(x-x’) where b=y’-mx’

m is the slope which is the differenec of the y points over the difference of the x points:

m=(1-3)/(2-6)=-2/-4=2/4=1/2

using th second equation

(y-y’)=m(x-x’), we get

(y-1)=1/2 (x-2)

or

y-1=1/2 x – 1

or

y=x/2

to check that lets plug int eh second point into that same equation

(y-y’)=m(x-x’)

(y-3)=1/2(x-6)

y-3=1/2 x – 6/2

y-3=1/2 x -3

y=x/2 QED

m = y2 – y1

———

x2 – x1

m = 3 – 1

——-

6 – 2

m = 2

—

4

So m= 1/2

Now, use slope-intercept form:

y = mx + b

and substitute either point (I’ll use the first one):

1 = 1/2(2) + b

1 = 1 + b

0 = b

So the equation is simply y = 1/2x. Done!

y=mx+b

1=.5(2)+b

b=1

y=(1/2)x+1