Equation of a Line Calculator | Point-Slope & Slope-Intercept Forms

Equation of a Line Calculator (Point-Slope, Slope-Intercept)

High School Equation of a Line Calculator

Generate the equation of a line in Slope-Intercept, Point-Slope, and Standard forms.

Slope-Intercept Form (y = mx + b)

Point-Slope Form (y – y₁ = m(x – x₁))

Standard Form (Ax + By = C)

Calculation Steps

Waiting for calculation…

Line Graph

The Line
Intercepts
Input Points

About the Equation of a Line Calculator

Linear equations serve as the foundation of algebra and analytic geometry. Consequently, a straight line can be described mathematically in several ways, with each form being useful for different situations. Furthermore, this tool helps you convert between these specific forms and visualizes the results effectively.

Common Forms of Linear Equations

  • Slope-Intercept Form (y = mx + b): Undoubtedly the most popular form. Here, m denotes the slope (rise/run) while b is the y-intercept (where the line crosses the y-axis). It is ideal for graphing.
  • Point-Slope Form (y – y₁ = m(x – x₁)): This is particularly useful when you know the slope and a specific point (x₁, y₁), yet you lack the y-intercept. It explicitly shows the shift from the origin.
  • Standard Form (Ax + By = C): Often utilized for solving systems of equations. Typically, A, B, and C are integers, and A is positive.

How to use the Equation of a Line Calculator

To begin, choose your input method based on the specific information you have available. For instance, use “Slope & Y-Intercept” when you have the slope and the vertical axis intercept. Alternatively, if you know the steepness and a single point, select “Point & Slope.” Finally, in cases where you only have two coordinates, choose “Two Points.” The calculator will subsequently handle the algebra to find m and b, identifying all three equation forms.

FAQ

Is this Equation of a Line Calculator free?

Yes, this tool is completely free and designed for students and teachers.

What if the line is vertical?

A vertical line has an undefined slope. Its equation is simply x = c. This calculator will detect vertical lines and display “x = [number]” instead of the standard y-forms.

Does the Equation of a Line Calculator handle fractions?

It processes inputs as decimals but can approximate fractional slopes. The standard form output typically approximates integers where possible.

How is the slope calculated?

Slope m = (y₂ – y₁) / (x₂ – x₁). It measures the steepness of the line.

HIGHER SCHOOL