Point Slope Form Calculator: Line Equation with Steps
This point slope form calculator writes a line as y − y1 = m(x − x1) from a point and slope or two points, then converts it to slope-intercept and standard form.
How to use
- Choose point and slope, or two points.
- Enter integers, decimals, or fractions such as 3/4. Type undefined when the slope of a vertical line is what you know.
- Read point-slope form, slope-intercept form y = mx + b, and standard form Ax + By = C with integer coefficients.
- Follow the steps under the result. A vertical line is x = a and has no slope. A horizontal line has slope 0.
Formula
Point-slope form is y − y1 = m(x − x1). From two points, m = (y2 − y1) / (x2 − x1). If x2 = x1, the slope is undefined and the line is x = x1. Slope-intercept form comes from distributing m and adding y1: y = mx + b, with b = y1 − m x1. Standard form clears denominators so Ax + By = C uses integers, then makes the leading coefficient positive.
Example. A line through (2, 1) with slope 3/4 is y − 1 = (3/4)(x − 2). That is y = (3/4)x − 1/2, and standard form 3x − 4y = 2.
Example. Points (1, 2) and (5, 5) have slope 3/4. Using (1, 2): y − 2 = (3/4)(x − 1), which is y = (3/4)x + 5/4, or 3x − 4y = −5.
Example. Points (3, 1) and (3, 4) share an x-value, so the slope is undefined and the line is x = 3.
Frequently asked questions
What is point-slope form?
Point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line.
How do I find point-slope form from two points?
First find the slope m = (y2 - y1) / (x2 - x1). Then plug m and either point into y - y1 = m(x - x1).
How do I convert point-slope form to slope-intercept form?
Distribute m across (x - x1), then add y1 to both sides to get y = mx + b.
What if the line is vertical?
A vertical line has an undefined slope, so it has no point-slope form. Its equation is x = a, where a is the shared x-value.
Can I enter fractions?
Yes. Enter values like 3/4 or -2/5 and the calculator keeps exact fractions in the answer where possible.
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