Two points determine a line, and everything about it falls out of one division: rise over run. This calculator delivers the full package — slope, equation, distance, midpoint, angle — with a live plot so the numbers stay attached to a picture.
From points to equation
Between (1, 2) and (5, 10): rise = 8, run = 4, slope m = 2. Plug either point into y = mx + b to find the intercept: b = 2 − 2(1) = 0, so the line is y = 2x. Positive slopes climb left-to-right, negative ones fall, zero is flat — and the sign is the first thing to check against the plot.
The vertical-line exception
Same x on both points means run = 0, and rise ÷ 0 has no value — the slope is undefined, not infinite. Vertical lines get their own notation, x = c, and the calculator switches to it rather than pretending. (Identical points get called out too: one point doesn't determine a line.)
Distance and midpoint ride along
The same coordinate differences power the other classics: distance is Pythagoras on (Δx, Δy) — √(4² + 8²) = √80 ≈ 8.94 here — and the midpoint is just the coordinate averages, (3, 6). One pair of subtractions, three theorems fed. The right-triangle view of that distance calculation lives in the triangle calculator.
Slope out in the world
Slope is grade on a road (a 6% grade is m = 0.06), pitch on a roof, rate on a graph — any "per" you can plot. Parallel lines share m; perpendicular ones multiply to −1 (slope 2 ⊥ slope −½). And when a line isn't straight, calculus asks this page's question at every point — but that's another site's territory. For parabolas, the quadratic calculator handles the curve.
Plot auto-scales to your points; math to double precision.