How do you find the equation of a line from two points?

First calculate the slope: m = (y2 - y1) / (x2 - x1). Then substitute one point into y = mx + b and solve for b: b = y1 - m * x1. The calculator does both steps automatically and also shows the rise, run, distance, midpoint, and angle.

What does the slope (m) tell you?

The slope tells you how steeply the line rises or falls. A slope of 2 means y increases by 2 for every 1 unit increase in x. A negative slope means the line falls left-to-right. A slope of 0 is a horizontal line. An undefined slope (when x1 = x2) is a vertical line.

What is the y-intercept (b)?

The y-intercept is the value of y when x = 0, i.e. the point where the line crosses the y-axis. In y = 3x + 5, the y-intercept is 5 — the line passes through (0, 5). You can find it by substituting any known point and the slope into y = mx + b and solving for b.

How do you solve for y (or x) on a line?

To find y given x, substitute the x value into y = mx + b and compute m * x + b. To find x given y, rearrange to x = (y - b) / m (valid as long as m is not zero). The "Solve for y" and "Solve for x" modes do this automatically and show the working.

What is the perpendicular slope?

Two lines are perpendicular when their slopes multiply to -1. So if a line has slope m, any line perpendicular to it has slope -1/m. The calculator outputs the perpendicular slope whenever the original slope is non-zero, which is useful for constructing right angles or normal lines in geometry problems.

Slope-Intercept Calculator

Q: What is slope-intercept form?

Slope-intercept form is the equation of a straight line written as y = mx + b, where m is the slope (rise over run) and b is the y-intercept (the y value where the line crosses the vertical axis). It is the most common way to express a linear equation because you can read off both key properties — steepness and position — at a glance.

The slope-intercept calculator turns any linear-equation input into a complete result set — equation, slope, y-intercept, angle, distance, midpoint, perpendicular slope, and a live SVG line diagram — all calculated locally in your browser with no data uploaded anywhere.

What is slope-intercept form?

A straight line in the plane can be written in several equivalent ways. The most useful is slope-intercept form:

y = mx + b

where m is the slope (rise ÷ run — how steeply the line climbs or falls) and b is the y-intercept (the y-coordinate where the line crosses the vertical axis). Once you know m and b you can immediately answer three questions: how steep is the line, where does it cross the y-axis, and what is y for any given x?

How the calculator works

The tool offers five modes so it covers every starting point you might have:

Two points → equation. Given P1 = (x1, y1) and P2 = (x2, y2) the slope is computed as m = (y2 - y1) / (x2 - x1), then the intercept follows from b = y1 - m * x1. From the same two points the tool also calculates the Euclidean distance sqrt((x2-x1)^2 + (y2-y1)^2), the midpoint ((x1+x2)/2, (y1+y2)/2), and the angle in degrees via arctan(dy/dx). If x1 = x2 the line is vertical and slope is undefined (x = constant).

m and b → equation. Supply the slope and y-intercept directly and the tool builds the full equation plus the angle and perpendicular slope.

Point + slope → equation. Given a known point (x0, y0) and slope m, the y-intercept is b = y0 - m * x0. The point-slope form y - y0 = m(x - x0) is also displayed alongside the standard form.

Solve for y. Given m, b and an x-value, the tool evaluates y = mx + b and shows the arithmetic working step by step.

Solve for x. Given m, b and a y-value, the tool rearranges to x = (y - b) / m (undefined when m = 0) and shows the working.

The SVG diagram plots the line across the visible data range, marks P1 and P2, draws the right-angle rise/run triangle when the two points are far enough apart to be legible, and overlays coordinate axes wherever they pass through the visible window.

Worked example

Suppose you have the points (1, 2) and (4, 8).

Rise = 8 - 2 = 6; Run = 4 - 1 = 3.
Slope m = 6 / 3 = 2.
Intercept b = 2 - 2 * 1 = 0.
Equation: y = 2x.
Angle: arctan(2) = 63.43°.
Distance: sqrt(3^2 + 6^2) = sqrt(45) ≈ 6.708.
Midpoint: ((1+4)/2, (2+8)/2) = (2.5, 5).
Perpendicular slope: -1/2 = -0.5.

Enter x = 10 into “Solve for y”: y = 2 * 10 + 0 = 20. Enter y = 14 into “Solve for x”: x = (14 - 0) / 2 = 7.

Formula reference

Quantity	Formula
Slope	m = (y2 - y1) / (x2 - x1)
Y-intercept	b = y1 - m * x1
Line equation	y = mx + b
Solve for y	y = mx + b
Solve for x	x = (y - b) / m
Distance	sqrt((x2-x1)^2 + (y2-y1)^2)
Midpoint	((x1+x2)/2, (y1+y2)/2)
Angle	arctan(m) in degrees
Perpendicular slope	-1/m

All calculations run entirely client-side — no numbers leave your device.