What does a negative slope mean?

The line falls as you move to the right. Reading left to right, a positive slope climbs and a negative one descends; zero is perfectly flat. In a graph of something over time, a negative slope is a decline - falling sales, cooling temperature, a draining tank.

How do I get the equation of the line?

It is shown under the slope, already simplified. The tool builds it from the slope and one of your points, then tidies it: a coefficient of 1 is left off, and a y-intercept of 0 disappears entirely, so you get y = 2x rather than y = 2x + 0.

Is the distance the same as the run?

No. The run is the sideways part only; the distance is the straight line between the two points, along the diagonal. From (0,0) to (3,4) the run is 3 but the distance is 5, because it follows the hypotenuse. On a hillside that is the difference between the map length of a path and the length you actually walk.

Can I use it for a roof pitch or a drain fall?

Yes. Treat the horizontal run as x and the drop as y: a fall of 25 mm over 3 metres is the pair (0,0) and (3000, −25) in millimetres, which gives a slope of about −0.0083, or roughly 1 in 120. Just keep both numbers in the same unit, or the ratio will be out by a factor of a thousand.

Slope Calculator - Gradient, Line Equation and Distance

2on / / Calculators / Math Calculators / Slope Calculator

Slope between two points

First point

x₁ y₁

Second point

x₂ y₂

Slope 2 y = 2x

Angle —

y-intercept —

Distance —

Midpoint —

What slope really measures

Slope is rise over run: how much the line climbs for every step it takes sideways. A slope of 2 means two units up for one across; a slope of −0.5 means half a unit down. The number is a rate, not a length, which is why the same slope describes a wheelchair ramp and a hillside road.

Using it in three steps

1 Type the coordinates of the first point, x then y.
2 Do the same for the second point. Order does not matter: swapping the two points gives the same slope.
3 Read the slope and the line equation at the top; the angle, intercept, distance and midpoint sit below.

Vertical lines have no slope

When both points share the same x, the run is zero and the formula would divide by it. This calculator says the slope does not exist instead of printing infinity, because infinity reads as "very steep" when the truth is that the question does not apply. The line still has an equation - it is just x = a number.

Slope as a percentage

Road signs and building codes usually quote slope as a percentage, which is simply the slope multiplied by a hundred: a gradient of 0.08 is an 8 percent grade. Accessibility rules for ramps are often written this way, and so are railway limits. The angle shown here is the same thing expressed in degrees - 8 percent is about 4.6 degrees, not 8.

Slope and line equations - frequently asked questions

No. Swapping the points flips the sign of both the rise and the run, and the two minus signs cancel. Distance and midpoint are unaffected too. The only thing that changes is nothing you can see, which is a useful check: if swapping them changes your hand-worked answer, a sign went astray.

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