Finding the slope of 2 points when those two points are fractions.?

Question

The two points are (-2/5, 2/5) and (4/3, 2/3). Someone told me the resulting slope is m = 2/13. If that is the case, I still don't know how he solved it because i never worked with fractions when finding the slope.

I know how to set up to solve for the slope. y-y/x-x or change in Y over change in x. Thats easy when i'm dealing with whole numbers.

But when i've never had to find the slope of two points that are fractions. In fact I've never had to solve a problem where i'm subtracting fractions that are part of a fraction itself. How do I solve a fraction that is over another fraction such as this?

[2/3 - 2/5] / [4/3 - (- 2/5)] or two thirds minus two fifths over four thirds minus negative two fifths.

Once I figure out how to get the slope, I can go ahead and put it into the point slope formula and solve without any assistance.

Answer 1

it's a bit harder to work with fractions but here it is:
find the least common denominator and in this case for both x and y it's 15. so first step to do is convert:
2/3 becomes 10/15
2/5 becomes 6/15
4/3 becomes 20/15
2/5 becomes 6/15
second step is to find the slope: change in y over change in x - so start with the y part:
10/15 - 6/15 = 4/15
the x part is:
20/15 - (-6/15) = 26/15
now you're having with fractions right? basically the x is on the bottom so all you need to do is flip the x fraction so that instead of it being divided, it gets multiplied:
(4/15) x (15/26) = 4/26 or 2/13.
Get it? if not you could first convert everything to decimals and use a calculator - it might be easier that way.

Answer 2

When you subract the fractions, make sure they have the same denominator.

2/3 = 10/15, 2/5 = 6/15 and 4/3 = 20/15, -2/5 = -6/15

10/15 - 6/15 = 4/15 20/15 - -6/15 = 26/15

4/15 divided by 26/15 is really just 4/15 times 15/26

4/15 x 15/26 = this is the slope! (60/402 = 30/201)

I hope I didn't mess anything up.

Answer 3

You have the answer, just plug in the fractions and use your calculator to find the answer. (y1-y2)/(x1-x2) It is really not as hard as you are trying to make it.

Answer 4

dont use your calculator the answer i got is -7/10, though i did not do this for a few years