what is the slope of the line that contains the points (-1,2) and (3,3)

Slope of a line is the change in y (rise) over the change in x(run).

The formula for m, slope,  is $${\mathtt{m}} = {\frac{\left({\mathtt{y2}}{\mathtt{\,-\,}}{\mathtt{y1}}\right)}{\left({\mathtt{x2}}{\mathtt{\,-\,}}{\mathtt{x1}}\right)}}$$

So just plug in your x and y values:

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

= 1/4

what is the slope of the line that contains the points (-1,2) and (3,3)

----------------------------------------------------------------------------------------------------------------------------

Slope is defined as  ⇒  "Change in y"  /   "Change in x" 

Here's a "non-technical" way to figure this....

How much did  "y" change by from the  first point to the second ???.....Answer... (+1) ....it increased from 1 to 2

How much did "x" change by from the first point to the second ???.....Answer... (+4).....it increased from -1 to 3

Therefore ..... Change in y"  /   "Change in x"   ⇒  (+1) / (+4)  = 1 / 4   ....and that's the "slope"

If either "x" or "y" had decreased (but not both), our slope would have been negative....

Thanks, kitty <3 !!!

Here's another way to do this....it's a "trick" I used to use when I tutored...

Take the points and "reverse" them.....we have (2, -1) and (3, 3)

Line them up like this and draw a line under them

(2 , -1)

(3 ,   3)

______      Now just "subtract" the "underneath" things from the things "overhead" - individually - like this

(2 , -1)

(-3 ,  - 3)

________

-1  ,  -4

Now.......put the thing in the first column "over" the thing in the second column   (-1) / (-4)  = 1 / 4 and Voila!!.......there's the "slope" 

I have reservations about your trick answer Chris, I won't be teaching it anytime soon - but hey, it works.  

I wish there were more emicons to choose from.

Here's another way to do this....it's a "trick" I used to use when I tutored...

Take the points and "reverse" them.....we have (2, -1) and (3, 3)

Line them up like this and draw a line under them

(2 , -1)

(3 ,   3)

______      Now just "subtract" the "underneath" things from the things "overhead" - individually - like this

 (2 , -1)

(-3 ,  - 3)

_______

-1  ,  -4

Now.......put the thing in the first column "over" the thing in the second column   (-1) / (-4)  = 1 / 4 and Voila!!.......there's the "slope" 

 

Let's take a look at this.

given (x1,y1), (x2,y2)

CPhil flips the coordinates to create (y1,x1) and (y2,x2) then subtracts to obtain

(y1-y2,x1-x2) and then creates (y1-y2)/(x1-x2)=(y2-y1)/(x2-x1) which is the usual slope formula.

It's Bona Fide!

Yes, yes, thanks Rom, I could see that it would work!