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Fractional slope from two points worksheets

Most slope sheets choose their points so the answer is a whole number, and a student can come away thinking that is what slopes do. These free printable worksheets give two points whose slope is a fraction, with an answer sheet.

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Fractional slope from two points
Fractional slope from two points worksheet — Slopes that do not come out whole, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The arithmetic is the familiar pair of subtractions, the second point minus the first, in the same order both times. The only new step is at the end. When 7 up for every 2 across does not divide evenly, the answer is the fraction 7/2, and that is finished work rather than a sign of a mistake.

Why this sheet works

Some fractions need simplifying and some do not, and some come out negative. Points in every quadrant mean that subtracting a negative comes up often, which is where most of the wrong answers on this page start. Writing out both subtractions keeps them visible.

How this one works

(−2, 6) and (6, 3)

(−2, 6)and(6, 3)
up=3 − 6 = −3
across=6 − (−2) = 8
m=−
  1. Slope is how far the line climbs for each step across. So take both differences between the two points — and take them in the SAME order, second minus first, both times.
  2. Going up: 3 − 6 = −3. Going across: 6 − (−2) = 8. Swapping the order on only one of those is what turns the sign the wrong way.
  3. −3 up for every 8 across does not come out whole, and it does not have to. The slope is the fraction −, already in lowest terms. So m = −.

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