Finding Slope From a Graph Worksheet With a Rise and Run Key

New lines on coordinate grids each time you press New sheet, with a key that draws the rise and run.

Slope from a graph

Name Date Score / 9

Find the slope of each line. Count the rise and the run between the two marked points.

  1. 1.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  2. 2.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  3. 3.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  4. 4.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  5. 5.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  6. 6.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  7. 7.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  8. 8.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

  9. 9.
    xy−6−5−4−3−2−11234560−6−5−4−3−2−1123456

    slope

Sheet HLIHF2 · Made at homeroomtools.com

Answer key: Slope from a graph

  1. 1. slope 1

    xy−6−5−4−3−2−11234560−6−5−4−3−2−112345611

  2. 2. slope −2

    xy−6−5−4−3−2−11234560−6−5−4−3−2−11234561−2

  3. 3. slope 4⁄3

    xy−6−5−4−3−2−11234560−6−5−4−3−2−112345634

  4. 4. slope 5⁄4

    xy−6−5−4−3−2−11234560−6−5−4−3−2−112345645

  5. 5. slope 3

    xy−6−5−4−3−2−11234560−6−5−4−3−2−112345626

  6. 6. slope 2⁄3

    xy−6−5−4−3−2−11234560−6−5−4−3−2−112345696

  7. 7. slope 3

    xy−6−5−4−3−2−11234560−6−5−4−3−2−112345613

  8. 8. slope −2⁄3

    xy−6−5−4−3−2−11234560−6−5−4−3−2−11234563−2

  9. 9. slope −4

    xy−6−5−4−3−2−11234560−6−5−4−3−2−11234561−4

Sheet HLIHF2 · 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.

9 problems on one page, plus the answer key. Sheet HLIHF2.

On the sheet
Problems
Grid
Slopes
Signs

Next step Next: find slope with no graph to count onThen name the slope in y = mx + b

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

The key for this free finding slope from a graph worksheet redraws each line with its rise and run dashed in. The sheet opens with 9 graphed lines, each through two marked points; students count both and write the slope.

Read the full guide

Find slope from graph worksheet: what students count

Every marked point sits where two grid lines cross, so both counts are whole numbers. The key redraws each graph with a dashed step between the points and writes the run and the rise beside it. Some pairs sit two or three steps apart, so the count needs reducing: a rise of 6 over a run of 9 is a slope of 2/3. A line that falls from left to right shows a negative rise.

Identifying slope from a graph worksheet in grade 8

Common Core standard 8.EE.6 has students use similar triangles to explain why the slope is the same between any two points on a line. Ask for a second slope triangle between two other grid points, then compare the two.

  • Tick Zero and undefined slopes before a quiz. About 1 line in 4 then runs flat or straight up.
  • Light Positive, negative, zero, undefined to add small sketches where students mark the kind of slope without counting.
  • Tick Ask for the y-intercept too once counting is secure. Each graph gets a second blank; the key gives both.

Questions and answers

Does the answer key show the rise and the run?

Yes. The key prints on its own page and redraws each graph with the dashed step, the run, the rise and the slope in lowest terms. A flat or vertical line gets no step, only slope 0 or slope undefined.

How do I make the sheet easier or harder?

For a first lesson set Slopes to Whole numbers and Signs to Positive only, and print 4 large graphs. Later choose Fractions with both signs. On the −6 to 6 grid 12 graphs fit one page and 16 take 2.

Can I use a bigger coordinate plane?

Yes. Switch Grid from −6 to 6 to −10 to 10. The squares get smaller, so 9 graphs still fit one page and 12 run to 2.

How many pages is the PDF?

With 9 graphs, 2: the sheet, then the key. 16 graphs make 3. Press Print and choose Save as PDF in your browser's print window; the pages fit Letter or A4.

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