How do I write a line from a point and its slope?

For point (2, 3) and slope 4, enter 4 for Slope, 2 for Point x and 3 for Point y. The point-slope form is y − 3 = 4(x − 2), and expanding gives y = 4x − 5. The standard-form output is −4x + y = −5, with the y coefficient normalized to 1.

Can I use two points instead of a known slope?

Choose Two points and enter both coordinate pairs. The calculator uses m = (y₂ − y₁) / (x₂ − x₁) and writes the point-slope form using the first point. For (1, 2) and (3, 6), m = 2 and y − 2 = 2(x − 1).

How do I enter negative or fractional values?

Use signed decimal numbers, such as −2 and 0.5. A point with y = −3 produces y + 3 on the left side, because subtracting a negative adds it. Fraction expressions such as 1/2 are not parsed in numeric fields; enter 0.5. Equation coefficients round to four decimal places.

What if the line is vertical?

A vertical line has no finite slope, so the point-plus-slope input cannot describe it. Enter two points sharing the same x in Two points to receive the undefined-slope explanation and equation x = that coordinate. A repeated point alone does not determine a line.

Point-Slope Form Calculator

Enter the slope m and one point (x₁, y₁) to write y − y₁ = m(x − x₁). The same line appears in slope-intercept and standard forms beside an equal-scale graph. If you know two points instead, select Two points; the calculator finds m before writing the forms.

Point + slope · slope = rise / run2slope63.43° · 200% grade

Mode

Slope

Point x

Point y

Enter a slope and a point on the line to get point-slope, slope-intercept and standard forms. Use decimal numbers, such as 0.5 for one half.

Sloperise / run
2
Y-interceptb in y = mx + b
0
Angledegrees above horizontal, arctan of the slope
63.4349488229°
Percent gradeslope × 100
200%
Equationy = mx + b, to four places
y = 2x + 0
Point-slope formusing the first point, coefficients to four places
y - 0 = 2(x - 0)
Standard formAx + By = C, B normalized to 1; four places
-2x + y = 0
Perpendicular slopenegative reciprocal, −1 / m
-0.5
Pitchrise per 12 of run
24:12

The same line in several forms. Slope is rise divided by run. The angle is the arctangent of the slope, in degrees above horizontal, so 45 degrees is a slope of 1. Percent grade is the slope times 100, the number a road sign uses. Distance is the straight length between the two points, from Pythagoras. The equation is the slope-intercept form y = mx + b, with b where the line crosses the y axis. And a roof pitch is the same slope written as the rise per 12 of run, so 6:12 is a slope of 0.5, a 50% grade and an angle of 26.57 degrees. A vertical line has no slope at all: the run is 0, and the tool says so instead of printing infinity.

Common questions

How do I write a line from a point and its slope?: For point (2, 3) and slope 4, enter 4 for Slope, 2 for Point x and 3 for Point y. The point-slope form is y − 3 = 4(x − 2), and expanding gives y = 4x − 5. The standard-form output is −4x + y = −5, with the y coefficient normalized to 1.
Can I use two points instead of a known slope?: Choose Two points and enter both coordinate pairs. The calculator uses m = (y₂ − y₁) / (x₂ − x₁) and writes the point-slope form using the first point. For (1, 2) and (3, 6), m = 2 and y − 2 = 2(x − 1).
How do I enter negative or fractional values?: Use signed decimal numbers, such as −2 and 0.5. A point with y = −3 produces y + 3 on the left side, because subtracting a negative adds it. Fraction expressions such as 1/2 are not parsed in numeric fields; enter 0.5. Equation coefficients round to four decimal places.
What if the line is vertical?: A vertical line has no finite slope, so the point-plus-slope input cannot describe it. Enter two points sharing the same x in Two points to receive the undefined-slope explanation and equation x = that coordinate. A repeated point alone does not determine a line.

Double-precision geometry from your numbers. Equations round coefficients to four decimal places; other readings show up to twelve significant digits. This calculates a line's geometry, not structural capacity or construction compliance.