Straight line equation calculator (y = mx + c)
Give the calculator two points and it returns everything a coordinate geometry question can ask for: the gradient, the equation in y = mx + c and in the general form ax + by + c = 0, the midpoint, the exact distance between the points, and the perpendicular bisector. Every value is worked out from your coordinates, including the awkward vertical-line case.
Enter two points A(x₁, y₁) and B(x₂, y₂)
y = 3x − 1
General form: 3x − 1y − 1 = 0
Gradient: 3
y-intercept: (0, -1)
Midpoint: (2.5, 6.5)
Length AB: 3√10 ≈ 9.486833
Perpendicular gradient: -1/3
Perpendicular bisector: y = -1/3x + 7.333333
The method behind it
- Gradient m = (y₂ − y₁) / (x₂ − x₁); a vertical line has an undefined gradient.
- Equation: y − y₁ = m(x − x₁), rearranged to y = mx + c or ax + by + c = 0.
- Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2); length = √((Δx)² + (Δy)²).
How to use this tool
1. Enter the first point
Type the x and y coordinates of point A. Negative and decimal coordinates are fine.
2. Enter the second point
Type the coordinates of point B. The two points must be different for a line to exist.
3. Use the form the question asks for
A Level questions often want ax + by + c = 0 with integer coefficients, while GCSE questions usually want y = mx + c. Both are shown.
Frequently asked questions
How do you find the equation of a line through two points?
Work out the gradient m = (y₂ − y₁) ÷ (x₂ − x₁), then substitute one point into y − y₁ = m(x − x₁) and rearrange into y = mx + c.
What is the gradient of a perpendicular line?
It is the negative reciprocal, −1/m. A line with gradient 2/3 is perpendicular to a line with gradient −3/2, and their product is always −1.
How do you find the distance between two points?
Use Pythagoras: distance = √((x₂ − x₁)² + (y₂ − y₁)²). Leave it in surd form on non-calculator papers.
What is a perpendicular bisector?
The line at right angles to a segment that passes through its midpoint. Find the midpoint, take the negative reciprocal of the gradient, then substitute into y − y₁ = m(x − x₁).
Practise this properly, not just once
A solver gives you the answer; exam marks come from the working. MathsGradeUp pairs exam-board questions with step-by-step feedback and revision notes on the exact topics you keep dropping marks on.