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Calculator Answers

Point Slope Form Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A point-slope form calculator is an algebraic tool that determines the equation of a straight line in the form y minus y₁ equals m multiplied by the quantity x minus x₁, where m represents the slope and (x₁, y₁) represents a known point on the line. The calculator processes inputs of a single coordinate point and a slope, or two coordinate points, and automatically solves for the resulting equation. It displays the step-by-step mathematical work and translates the output into slope-intercept form. Algebra students use this tool to verify geometry homework.

Pick slope-plus-point or two-points input. The calculator returns the point-slope equation y − y₁ = m(x − x₁) along with the slope-intercept form and the slope itself.

See also: Slope Calculator, Slope Intercept Form Calculator, and y = mx + b Calculator.

Quick Answer

Find the point-slope form equation of a line. Enter the slope (m) and a coordinate point (x₁, y₁) to calculate the linear equation.

From

Point-slope form sits between "slope" and "slope-intercept": it captures both the slope and a specific point in one equation. Solve for y to convert to slope-intercept form.

Point-slope

Point-slope form

y − 4 = 2(x − 3)

Slope m = 2; through (3, 4)

Slope m2
Point(3, 4)
Slope-intercept formy = 2x - 2
y-intercept b-2

Use point-slope form when you know the slope and a specific point but not the y-intercept. Distribute m and add y₁ to both sides to convert to slope-intercept form.

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Examples

Slope 2, point (3,4)

y − 4 = 2(x − 3); y = 2x − 2

Two points (1,2), (4,11)

m = 3; y − 2 = 3(x − 1); y = 3x − 1

Slope −0.5, point (0,5)

y − 5 = −0.5(x); y = −0.5x + 5

Horizontal: slope 0, point (2,7)

y − 7 = 0; y = 7

How it works

Point-slope form is the equation built directly from the slope and a known point. It comes from rearranging the slope formula: if (x, y) is any point on the line and (x₁, y₁) is a known point, then (y − y₁) / (x − x₁) = m.

Point-slope · y − y₁ = m(x − x₁)

Two-point slope · m = (y₂ − y₁) / (x₂ − x₁)

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Slope CalculatorFind the slope of the line through two points using m = (y₂ − y₁) / (x₂ − x₁), or give a slope and three coordinates and solve for the fourth. Handles positive, negative, zero, and undefined (vertical) slopes, and reports the angle, grade, ratio, and line equations.Slope Intercept Form CalculatorBuild the slope-intercept equation y = mx + b from two points, a slope and one point, or a standard-form equation Ax + By = C. Returns the slope, y-intercept, and step notes.y = mx + b CalculatorFind the slope-intercept form of a line from two points, point-slope, or slope and y-intercept.Interpolation CalculatorEstimate a y value between two known points using the linear interpolation formula. Shows the working and flags when the target x falls outside the known range.

Frequently asked questions

y − y₁ = m(x − x₁). It is a way to write the equation of a line using its slope m and any one point (x₁, y₁) on the line. The form makes it easy to plug in a point you already know.

Point-slope is best when you know a specific point and the slope but not the y-intercept (b in y = mx + b). It is also the natural form to write when a problem hands you a point and a slope directly.

Distribute m on the right side, then add y₁ to both sides. The calculator does this and shows the slope-intercept equivalent next to the point-slope form.

First compute the slope m = (y₂ − y₁) / (x₂ − x₁). Then pick either point and substitute into y − y₁ = m(x − x₁). The calculator handles both steps.

A vertical line has undefined slope. Point-slope form y − y₁ = m(x − x₁) needs a finite m, so vertical lines can only be written as x = constant. The calculator detects this case and flags it.