Line Equation Calculator – Guide & Formulas
Find the equation of a line passing through two points or given a point and a slope. Generates slope-intercept, point-slope, and standard equations.
Calculate the mathematical equation of a line. Supports inputting two coordinate points, or a single coordinate point and a known slope value.
Key Takeaway
Use the free Line Equation Calculator to find the equation of a line passing through two points or given a point and a slope. generates slope-intercept, point-slope, and standard equations. Get instant results with step-by-step explanations.
How to Use the Line Equation Calculator
- Choose your input method: Two Points or Point and Slope.
- Enter the numerical values in the fields.
- Analyze the generated Slope-Intercept (y = mx + b), Point-Slope, and Standard (Ax + By = C) equations.
The Formula
Variable Definitions
- m: Slope of the line
- b: Y-intercept (where line crosses vertical axis)
- (x1, y1): A point positioned on the line
Determining the Equation of a Line
Find the linear equation of a line passing through points (2, 5) and (4, 9).
- Step 1: Calculate slope m = (9 - 5) / (4 - 2) = 4 / 2 = 2.
- Step 2: Use point-slope form with (2, 5): y - 5 = 2(x - 2).
- Step 3: Rearrange to slope-intercept form: y = 2x - 4 + 5 => y = 2x + 1.
- Step 4: Standard form is: -2x + y = 1 (or 2x - y = -1).
Frequently Asked Questions
What is the standard form of a linear equation?
The standard form is Ax + By = C, where A, B, and C are integers, and A should ideally be non-negative.
How do you find the x-intercept of a line equation?
Set y = 0 and solve the equation for x. In y = mx + b, the x-intercept is -b/m.
What if the line is vertical?
A vertical line has no y-intercept (unless it is the y-axis itself) and its equation is simply represented as x = k, where k is the x-coordinate of all points on the line.