Slope Calculator

Type two points, click Calculate. This slope calculator gives the slope, the y-intercept, and the line's equation instantly, right on the page.

• First point, x and y — the coordinates of your first point, such as $(1, 2)$ in the calculator's default
• Second point, x and y — the coordinates of your second point, such as $(4, 8)$

You immediately get two results: the slope m (the rise over run between your points) and the y-intercept b of $y = mx + b$. With the defaults, the slope calculator returns $m = 2$ and $b = 0$: the line $y = 2x$.

This page is more than a static slope calculator — it is also an AI tutor you can ask questions:

• Ask in plain words. “What is the slope of the line through (1, 2) and (4, 8)?” The AI reads it and solves it step by step.
• Take a photo of your homework. No typing: the AI reads the points and shows every step.
• Ask about the ideas, not just the number. “Why is a vertical line's slope undefined?” The AI explains — and you can check every number against the slope calculator on this page, so nothing is guessed.
• Work backwards, then keep asking. Give a slope and a point, and ask for the line. Follow-up questions are welcome, so ask “why?” as often as you need: the slope calculator page keeps teaching.

Slope is rise over run: how far a line climbs (or falls) for each step you take to the right. Move 1 unit right along a line with slope 2 and you rise 2 units. Move 1 unit right along a line with slope $-2$ and you drop 2 units. One number carries both the steepness and the direction of a line — that is what a slope calculator reads out.

Every line lands in one of four cases:

• Positive slope — the line rises from left to right, like $y = 2x$.
• Negative slope — the line falls from left to right, like $y = -2x + 5$.
• Zero slope — a horizontal line, like $y = 5$: no rise at all, so $m = 0$.
• Undefined slope — a vertical line, like $x = 3$: no run to divide by, so the slope does not exist.

The last pair is where most slips happen. Horizontal means slope 0 — fine. Vertical means undefined, not 0. Enter two points that share one x into the slope calculator and it tells you exactly that: the line is vertical, and no single number describes its steepness.

Two points are all a slope calculator needs. The vertical change between them is the rise, the horizontal change is the run, and the slope is their quotient:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

One discipline and one only: pick which point is first and stay with it. The rise and the run must both subtract in the same direction — that habit keeps the sign of $m$ honest, and the slope calculator follows it automatically.

One guarantee comes with the formula: a straight line has exactly one slope. Pick any two points on the same line and the slope calculator returns the same $m$ every time. So it never matters which pair of points you grabbed from the line — and one point plus the slope is enough to draw the whole thing.

Find the slope and the equation of the line through $(1, 2)$ and $(4, 8)$ — the slope calculator's default points.

1. Rise: $y_2 - y_1 = 8 - 2 = 6$.
2. Run: $x_2 - x_1 = 4 - 1 = 3$.
3. Slope: $m = \dfrac{6}{3} = 2$. Every 1 unit right, the line climbs 2 units.
4. y-intercept: $b = y_1 - m x_1 = 2 - 2 \times 1 = 0$.

So the line is $y = 2x + 0$, or just $y = 2x$ — it passes straight through the origin. Read $m = 2$ as rise over run: from $(1, 2)$, step 3 units right and 6 units up — run 3, rise 6 — and you land exactly on $(4, 8)$. The slope is the directions between your two points, nothing more.

Check it against the second point: when $x = 4$, $y = 2 \times 4 = 8$. Point $(4, 8)$ is on the line, exactly as given. Click Calculate above and the slope calculator walks all four steps with you.

Negative slopes run the same route — the arithmetic just carries a minus sign. Take the line through $(0, 5)$ and $(2, 1)$.

1. Rise: $1 - 5 = -4$.
2. Run: $2 - 0 = 2$.
3. Slope: $m = \dfrac{-4}{2} = -2$. The line drops 2 units for every 1 unit right.
4. y-intercept: $(0, 5)$ sits on the y-axis, so $b = 5$ — or compute it: $b = y_1 - m x_1 = 5 - (-2)(0) = 5$.

The line is $y = -2x + 5$. Now the general move from any slope to a full equation. With a point $(x_1, y_1)$ and slope $m$, point-slope form writes the line at once:

$y - y_1 = m(x - x_1)$

Expand and collect: $y - 5 = -2(x - 0)$ becomes $y = -2x + 5$ — slope-intercept form again. Use point-slope when you know a point, slope-intercept when you want to read $m$ and $b$ fast; the slope calculator above hands you both.

1. Flipping rise and run. Slope is rise over run — y-change over x-change, $\dfrac{\Delta y}{\Delta x}$. Divide the run by the rise and you get the reciprocal: a different number. Keep $y_2 - y_1$ on top.
2. Subtracting in mixed order. If the rise uses $y_2 - y_1$, the run must use $x_2 - x_1$. Compute one forwards and the other backwards and the sign of your slope flips. Subtract in the same direction both times.
3. Confusing zero with undefined. A horizontal line has slope 0 (the rise is 0). A vertical line's slope is undefined (the run is 0). The slope calculator labels the vertical case instead of guessing.

One habit catches all three: write the formula, substitute with parentheses, simplify. That is the exact sequence the slope calculator above runs — compare your working line by line.