Point Slope Form Calculator
This point slope form calculator builds the equation of a line from two points or from one point and the slope. Example: the line through (1, 2) and (3, 8) is y − 2 = 3(x − 1), which is y = 3x − 1.
Source: Wikipedia – Lineare Funktion. Updated: .
How it is calculated
The point slope form describes a line through a known point (x₁, y₁) with slope m: y − y₁ = m·(x − x₁). It is handy because the point and slope can be read off directly, and it converts easily into the slope-intercept form y = mx + b.
Method
If two points are given, first compute the slope m = (y₂ − y₁) / (x₂ − x₁). Then insert m and one of the points into the formula. For the slope-intercept form, solve for y: y = m·x + b with b = y₁ − m·x₁. The x-intercept follows from 0 = m·x + b as x = −b / m. The calculator handles both routes and shows each step.
Examples
Through (1, 2) and (3, 8): m = 6 / 2 = 3, so y − 2 = 3(x − 1), and expanded y = 3x − 1; the x-intercept is x = 1/3. With m = 2 through (3, 5) you get y − 5 = 2(x − 3), that is y = 2x − 1. If both points share the same x-coordinate the line is vertical, has the equation x = c and no slope.
- A negative sign on y₁ or x₁ becomes a plus in the bracket: the point (−2, −3) gives y + 3 = m(x + 2).
- If m = 0 the line is horizontal, y = b, and has no x-intercept (unless it lies on the x-axis).
Frequently asked questions
What is point slope form?
The line equation y − y₁ = m(x − x₁) with slope m and a point (x₁, y₁) on the line.
How do I turn it into slope-intercept form?
Expand the bracket and add y₁: y = m·x − m·x₁ + y₁. The constant term is b = y₁ − m·x₁.
Why is there no point slope form for vertical lines?
Because the slope would divide by zero and is undefined. Vertical lines are written as x = c.
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