Slope Sketch

SLOPE CALCULATOR / EXPLORE THE CONNECTION

Every line
has a story.

Move the points. See how the slope,
equation and geometry connect.

THE COORDINATE DESKrise / run
— run (horizontal change)— rise (vertical change)

Set your points

Enter coordinates to see the slope and equation.

POINT 1 · A
POINT 2 · B
EXPLORE A DIFFERENT LINE

Drag a point or focus it and use arrow keys. Each step moves half a unit.

WORKED EXAMPLE
m = 1/2

Rise = 4 − 2 = 2. Run = 5 − 1 = 4.

y = (1/2)x + 3/2

Exact fractions · line equation · rise & runNo account. No uploads.

KEEP EXPLORING

Small steps.
Big ideas.

  1. 01The slope formula
  2. 02Rise over run
  3. 03Slope-intercept form
  4. 04Point-slope form
  5. 05Zero or undefined?
  6. 06Positive & negative slope
  7. 07Parallel & perpendicular

What does slope tell you?

Slope measures the change in y for each unit change in x along a straight line. A positive slope rises from left to right; a negative slope falls. Zero slope is horizontal, and a vertical line has undefined slope.

m = (y₂ − y₁) / (x₂ − x₁)

The run must be nonzero for a numerical slope. Two identical points do not determine a unique line. This tool distinguishes those cases and plots the points, rather than returning an inaccurate number.

Designed for algebra and graphing, with uses in data interpretation too. The graph is illustrative and does not certify construction grades or engineering dimensions.

From slope to an equation

For A = (1, 2) and B = (5, 4), the rise is 2 and the run is 4. So m = 2/4 = 1/2.

Substitute A into y = mx + b: 2 = (1/2) × 1 + b. This gives b = 3/2.

y = (1/2)x + 3/2

Check the other point: (1/2) × 5 + 3/2 = 4. For more, read slope-intercept form and rise over run.

Questions & answers

How do I calculate slope from two points?

Subtract the first y coordinate from the second, then divide by the second x coordinate minus the first: m = (y₂ − y₁)/(x₂ − x₁). Keep the same point order in both subtractions.

Can I use fractions and negative coordinates?

Yes. Enter values such as -2, 0.75, 3/4, or 1 1/2. Calculations use exact fractions. The graph uses approximate coordinates and may omit extremely large or closely spaced values.

Why does my result say undefined?

If the x coordinates are equal but the y coordinates differ, the run is zero. The line is vertical and division by zero is undefined. Its equation is x = the common x coordinate.

What happens if both points are the same?

A single point does not determine a unique line. The calculator identifies repeated points instead of calling the slope zero.

Does the graph have equal axis scales?

Yes. One coordinate unit has the same visual length on both axes. The view fits the entered points, so the origin may be outside the displayed window.

Are my coordinates uploaded or stored?

No. This calculator runs in your browser without an account. It does not upload or save your coordinate entries or practice answers.