Draw Slope Triangles: Rise Over Run Worksheet

Algebra and Function Practice

Slope measures steepness as rise over run. A slope triangle makes that ratio visible: pick two points on a line, draw a right triangle with a vertical leg (rise) and a horizontal leg (run), then divide. This lesson teaches a consistent drawing convention so your triangle clearly shows direction and distance. You will practice reading coordinates, counting grid units, labeling legs, and simplifying fractions. All examples use integer coordinates on square grids, so counts are exact and easy to check. The convention: draw the vertical leg first from the left point, then the horizontal leg to the right point, and mark the right angle at the corner. Rise is positive upward and negative downward; run is positive rightward and negative leftward. When both legs are drawn, the slope is rise divided by run, simplified. Letter styles and handwriting vary, so the rubric accepts any legible labels and correct counts, not one exact drawing style.

Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.

Set up the grid and choose two points

A coordinate grid has evenly spaced vertical and horizontal lines. Each intersection is a point (x, y). To draw a slope triangle, first mark two points that lie on the same straight line. Choose points where the line crosses grid intersections so counts are whole numbers. Label the left point A and the right point B. If the line goes downward from left to right, B will be lower than A; that is fine.

Record coordinates before drawing. For A at (1, 2) and B at (4, 6), the x-values differ by 3 and the y-values differ by 4. These differences become the legs of the triangle. Keep units consistent: one grid square equals one unit in both directions unless the grid states otherwise.

1. Mark A and B on the line at grid intersections.
2. Write A(x1, y1) and B(x2, y2) beside the grid.
3. Subtract x-values: run = x2 - x1.
4. Subtract y-values: rise = y2 - y1.

Draw the right triangle and label legs

From A, draw a vertical segment to the height of B. Then draw a horizontal segment from that corner to B. The corner where the two legs meet is the right angle. This convention always puts the right angle at the same relative corner: vertical leg first, then horizontal leg toward B. If B is below A, the vertical leg goes downward and rise is negative.

Label the vertical leg with the rise value and the horizontal leg with the run value. Write rise above the vertical leg and run below the horizontal leg, or beside each leg. Any legible placement is acceptable. Do not label the hypotenuse as rise or run; the hypotenuse is the line segment between A and B.

1. Draw the vertical leg from A to the corner.
2. Draw the horizontal leg from the corner to B.
3. Mark the right angle at the corner.
4. Label rise on the vertical leg and run on the horizontal leg.

Compute and simplify slope

Slope equals rise divided by run. Using A(1, 2) and B(4, 6): rise = 6 - 2 = 4 and run = 4 - 1 = 3, so slope = 4/3. The fraction is already simplified because 4 and 3 share no common factor other than 1. If rise and run share a common factor, divide both by it. For example, rise 6 and run 4 give 6/4 = 3/2.

Check the sign: a line rising left to right has positive slope; falling left to right has negative slope; horizontal has slope 0; vertical has undefined slope because run is 0. Always state the simplified fraction and the sign.

1. Write slope = rise / run with the counted values.
2. Simplify by dividing numerator and denominator by their greatest common factor.
3. Check the sign against the line direction.
4. Record the final slope as a simplified fraction.

Verify with a second triangle

A useful check is to draw a second slope triangle between a different pair of points on the same line. The rise and run counts may differ, but the simplified slope must match. For the line through (1, 2) and (4, 6), choose (1, 2) and (7, 10): rise = 8, run = 6, slope = 8/6 = 4/3. The match confirms the first result.

This check also catches counting errors. If the second simplified slope differs, recheck coordinates and leg lengths before changing the answer.

1. Choose another pair of grid-intersection points on the line.
2. Draw and label a second triangle using the same convention.
3. Compute and simplify the second slope.
4. Compare simplified slopes; they should be equal.

Worked example

A line passes through A(2, 1) and B(5, 7). Draw a slope triangle using the convention, label rise and run, and compute the simplified slope.

Four practice exercises

Common mistakes

• Counting grid lines instead of grid intervals. Count spaces between intersections, not the lines themselves. From x = 1 to x = 4 there are 3 intervals, so run = 3.
• Swapping rise and run in the fraction. Rise is the vertical change (y-values); run is the horizontal change (x-values). Write slope = rise / run and label legs before dividing.
• Ignoring negative direction. If the line falls from left to right, rise is negative. Keep the negative sign in the fraction and simplify.
• Leaving the fraction unsimplified. Divide numerator and denominator by their greatest common factor. For 8/6, divide by 2 to get 4/3.

Self-check rubric

• Two points on the line are correctly identified and labeled with coordinates.
• The right triangle follows the convention: vertical leg from the left point, horizontal leg to the right point, right angle marked.
• Rise and run are labeled on the correct legs with correct integer counts.
• Slope is written as rise divided by run and simplified correctly.
• Sign of the slope matches the line direction.
• Labels are legible; alternative handwriting styles and label placements are accepted if the meaning is clear.

Questions and answers