if you look at the two points… you can see just from looking at the coordinates that the line is y = 1…. why? Because those two points fall on the horizontal line “y = 1” since they both have “1” as their y-coordinates…

If you didn’t realize that… then what you did is okay… because that’s what you would do for any problem that gives you two given points… You would first find m… like you did…

The next step is to use the general line equation format…y = mx + b…. And find your “b” (the y-intercept which is where the line crosses the y-axis).

So your m = 0… which means you are left with…

y = (0)x + b ** when you substitute 0 for “m”)

y = b….

Now plug in the y-coordinate of “one” of the points… either one…

And you find b = 1….

Now… put that back into your “general” y = mx + b equation…

And you have….

y = (0)x + 1

y = 1….

So that’s what you would do anyway had the points been like (2, 1) and (-2, 3) that did not fall on either a horizontal or vertical line… but a line that is slanty…

Hope this helps! You are definitely on the right track!!!

In the problem that I gave… it would be solved this way…

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

so your ” y = mx + b” becomes y = -(1/2)x + b….

Now you have to find “b”….

So you would take one point and plug in the x-coordinate and y-coordinate of the SAME point… like this…

I will choose point ( -2, 3)…. so the x-coordinate is -2 or “x = -2” and the y-coordinate is “y = 3”

So…. our y = -(1/2) x + b…. becomes…

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

3 = 1 + b

b = 2…

put that into your y = -(1/2)x + b equation… and you have…

y = -(1/2)x + 2

How do you know that this is correct? Plug in the x-coordinate and y-coordinate of the SECOND point…. (2,1)…. where x = 2 and y = 1… like this…

y = -(1/2)x + 2

1 = -(1/2)(2) + 2…. Is this true?

1 = -1 + 2

1 = 1…. YES!!!

So you did everything correctly and y = -(1/2)x + 2 for my problem would be the equation for the line that runs through my two given points….