Slope Calculator

m = (y₂ − y₁) ÷ (x₂ − x₁), the vertical change divided by the horizontal change, rise over run. The order doesn't matter as long as it's consistent: subtracting point 1 from point 2 in both numerator and denominator gives the same m as the reverse. The classic error is mixing orders (y₂ − y₁ over x₁ − x₂), which flips the sign, if your slope's sign disagrees with the picture (line clearly going uphill, negative m), that's the bug.

Push either known point through y = mx + b to find b: with m = 2 and point (1, 5), 5 = 2·1 + b gives b = 3, so y = 2x + 3. Alternatively use point-slope form directly, y − y₁ = m(x − x₁), which some teachers require and which needs no solving step. Both describe the same line; the calculator shows slope-intercept because it's the form that reads instantly (slope and y-crossing visible at a glance).

Because the run is zero and division by zero has no value, not a very large value. It's also directionless: approaching vertical from the left, slopes race toward +∞; from the right, toward −∞, so no single number works. Vertical lines are the one case y = mx + b can't express; they're written x = c instead. Distinct from zero slope, which is a perfectly ordinary horizontal line. Mixing those two up is a reliable test-point loss.

Three languages for the same steepness. Slope is the raw ratio (0.08), grade is that ratio as a percentage (8%, what road signs use), and the angle is arctan of the slope (4.6°). The counterintuitive one: a 100% grade is only 45°, not vertical, because it means equal rise and run. The calculator's angle output does the arctan for you. Useful for ramps (ADA maximum is 1:12, about 4.8°) and roof pitch conversations.