Finding Slope From Two Points Worksheet for the Slope Formula

Pairs of points and no graph: students substitute into the slope formula, and every new sheet prints with its key.

Slope from two points

Name Date Score / 10

Find the slope of the line through each pair of points.

  1. 1.

    (8, −2) and (2, −4)

    slope

  2. 2.

    (−1, −7) and (2, −4)

    slope

  3. 3.

    (−5, −6) and (−2, −8)

    slope

  4. 4.

    (−8, 8) and (−10, 3)

    slope

  5. 5.

    (−3, −1) and (−1, 5)

    slope

  6. 6.

    (−3, 0) and (1, −2)

    slope

  7. 7.

    (3, 2) and (5, −4)

    slope

  8. 8.

    (1, 3) and (−1, −3)

    slope

  9. 9.

    (9, 3) and (8, 0)

    slope

  10. 10.

    (1, 1) and (−1, 9)

    slope

Sheet YOLPDY · Made at homeroomtools.com

Answer key: Slope from two points

  1. 1. 1⁄3

  2. 2. 1

  3. 3. −2⁄3

  4. 4. 5⁄2

  5. 5. 3

  6. 6. −1⁄2

  7. 7. −3

  8. 8. 3

  9. 9. 3

  10. 10. −4

Sheet YOLPDY · answer key · Made at homeroomtools.com

Scroll the preview to see every page. Paper copies fit US Letter and A4 and need no colour ink.

10 problems on one page, plus the answer key. Sheet YOLPDY.

On the sheet
Problems
Slopes
Signs
Points

Next step Next: write the equation through two pointsGo back a step: count rise and run on a graph

Slope and line facts behind every answer key

Show the table

Every line on these sheets goes through grid points with whole-number coordinates, so a slope can be counted off the graph square by square. The key is worked out with whole-number arithmetic and every slope is given in lowest terms.

IdeaWhat it says
Sloperise over run: the change in y divided by the change in x, m = (y₂ − y₁) ÷ (x₂ − x₁)
Slope-intercept formy = mx + b, where m is the slope and b is the y-intercept, the point (0, b) where the line crosses the y-axis
Positive and negativea line that climbs from left to right has a positive slope; one that falls has a negative slope
Zero slopea horizontal line, y = b: it rises by nothing, however far it runs
Undefined slopea vertical line, x = a: its run is 0, and nothing can be divided by 0
From a tablepick any two rows: the difference of the y values over the difference of the x values, in the same order
Standard formAx + By = C. Put y = 0 to find the x-intercept, C ÷ A, and x = 0 to find the y-intercept, C ÷ B
From a point and a slopeput the point into y = mx + b and solve for b: b = y − mx

A short code sits at the foot of every sheet and of its answer key, so loose pages can be matched. The share link rebuilds that sheet, number for number: a key printed next week still fits the copies handed out today.

How it works

No graph to count on: this finding slope from two points worksheet gives 10 pairs such as (8, −2) and (2, −4). Students subtract the y values, subtract the x values and divide. An answer key follows.

Read the full guide

Make it a slope formula worksheet

Tick Print the slope formula to fill in and a blank formula prints under every pair: four empty boxes set as a fraction, then a line for the answer. The instruction asks students to fill in (y₂ − y₁) ÷ (x₂ − x₁) first, so the substitution is on paper before anyone simplifies.

Find the slope of two points worksheet: the sign slips to watch

In about half the pairs the second point sits left of the first, so the run comes out negative. (8, −2) and (2, −4) give −2 over −6, which is 1/3. Swap the order in only one subtraction and the answer flips to −1/3. Common Core standard 8.F.4 has students find a rate of change from two (x, y) values, the skill this sheet drills.

  • Choose First quadrant only for a first lesson. Every coordinate is then 0 to 10, so nobody subtracts a negative.
  • Tick Zero and undefined slopes to mix in pairs like (2, 6) and (2, 8), where the run is 0.
  • Light Equation from a point or two when the class is ready to turn a slope into y = mx + b.

Questions and answers

Does the finding slope from 2 points worksheet have an answer key?

Yes. The key prints on its own page after the sheet and gives each slope in lowest terms, such as 5/2 or −3. It does not show the subtraction, so have students write theirs out.

How many problems fit on a page?

Choose 6, 10, 12, 15 or 20; each fits one page of Letter or A4. With the formula printed under each pair, 12 still fit and 15 or 20 take 2 pages. For a PDF, choose Save as PDF in your browser's print window.

Do the slopes come out as fractions?

Set Slopes to Whole numbers for answers from 1 to 5 or their negatives. Fractions gives answers such as 1/3 or −5/2, with denominators from 2 to 5. Both mixes the two. Signs set to Positive only removes the falling lines.

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