Slope Drills: Rise Over Run Practice

Algebra and Function Practice

Slope measures steepness as vertical change divided by horizontal change. This drill set focuses on computing slope from graphed lines or two points using rise over run. You will practice reading coordinates, counting grid units, and simplifying fractions. The convention here is that rise is the change in y (up positive, down negative) and run is the change in x (right positive, left negative). Always subtract coordinates in the same order: slope equals (y2 minus y1) divided by (x2 minus x1). When reading a graph, pick two clear points on the line, count the vertical units between them, count the horizontal units, and write rise over run. Simplify the fraction and note the sign. A positive slope rises left to right; a negative slope falls left to right. Horizontal lines have slope zero; vertical lines have undefined slope. The worked example and four exercises use simple integer coordinates so you can check arithmetic easily. Use the rubric to self-assess accuracy, sign, simplification, and labeling. The planned drill sheet will contain twelve mixed items with a rise/run workspace and a separate answer key; it is not yet built.

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

Reading Slope from a Graph

Choose two points where the line crosses grid intersections. Label the left point (x1, y1) and the right point (x2, y2). Count the vertical change from y1 to y2: up is positive, down is negative. Count the horizontal change from x1 to x2: right is positive, left is negative. Write rise over run as a fraction, then simplify. For example, if a line passes through (1, 2) and (4, 8), rise is 8 minus 2 equals 6, run is 4 minus 1 equals 3, so slope is 6/3 equals 2. If the line falls, the rise is negative and the slope is negative.

1. Pick two grid-intersection points on the line.
2. Subtract y-coordinates in the same order to get rise.
3. Subtract x-coordinates in the same order to get run.
4. Write rise/run and simplify.
5. Check the sign against the line direction.

Computing Slope from Two Points

When two points are given, use the formula slope equals (y2 minus y1) divided by (x2 minus x1). Keep the order consistent: if you subtract y1 from y2, subtract x1 from x2. A common error is reversing one subtraction but not the other, which flips the sign. After computing, simplify the fraction by dividing numerator and denominator by their greatest common factor. If the denominator is zero, the slope is undefined because the line is vertical. If the numerator is zero, the slope is zero because the line is horizontal.

1. Write the two points as (x1, y1) and (x2, y2).
2. Compute rise = y2 - y1.
3. Compute run = x2 - x1.
4. Divide rise by run and simplify.
5. State whether the slope is positive, negative, zero, or undefined.

Checking Your Slope Work

A quick check is to move from one point to the other using the simplified slope. For slope 2, from (1, 2) move up 2 and right 1 to reach (2, 4); if that point is also on the line, the slope is consistent. For a negative slope, move down and right. Another check is to substitute both points into the rise-over-run fraction and confirm the same simplified value. Always include units only if the axes have units; otherwise slope is unitless. Label rise and run clearly in your workspace so a reader can follow your reasoning.

1. Use the simplified slope to step from one point to the other.
2. Confirm the second point lies on the line or matches the given pair.
3. Recompute with the formula to catch sign errors.
4. Label rise and run in your written work.

Worked example

Find the slope of the line through (2, 1) and (6, 9).

Four practice exercises

Common mistakes

• Subtracting coordinates in inconsistent order, such as y2 minus y1 but x1 minus x2. Subtract both coordinates in the same order: (y2 - y1) over (x2 - x1).
• Counting run as vertical and rise as horizontal. Rise is vertical change (y), run is horizontal change (x).
• Forgetting to simplify the fraction. Divide numerator and denominator by their greatest common factor.
• Dropping the negative sign when the line falls left to right. Check the direction: falling line means negative slope.

Self-check rubric

• Correctly identifies rise and run from the graph or point pair.
• Uses consistent subtraction order for both coordinates.
• Simplifies the fraction fully.
• States the correct sign and type (positive, negative, zero, undefined).
• Shows labeled workspace with rise and run.
• Accepts valid alternative point choices that yield the same simplified slope.

Questions and answers