1. The Basics: What is a Linear Equation?
A linear equation is an equation that represents a straight line on a graph. It can be written in several forms, each highlighting different properties of the line like its steepness (slope) or where it crosses the axes (intercepts). This section introduces the two most common forms.
Slope-Intercept Form: y = mx + b
This is often the most useful form for graphing. It directly tells you the slope and the y-intercept.
m = Slope
The slope measures the steepness of the line. It's the "rise" (vertical change) over the "run" (horizontal change).
b = Y-Intercept
The y-intercept is the point where the line crosses the vertical y-axis. Its coordinate is (0, b).
Standard Form: Ax + By = C
In this form, A, B, and C are integers. It's useful for finding intercepts quickly and for solving systems of linear equations.
A, B, C
These are coefficients and constants. 'A' should preferably be non-negative.
Finding Intercepts
Set y=0 to find the x-intercept. Set x=0 to find the y-intercept.
Calculating Slope
The slope (m) can be found using the formula m = -A / B.
2. Interactive Calculator & Visualizer
The best way to understand a linear equation is to see it in action. Use the controls below to change the parameters of the equation and watch how the graph changes in real-time. This tool helps you build an intuition for how slope and intercepts define a line.
Calculate from Slope & Intercept
Calculate from Two Points
Resulting Equation
3. Solving a Linear Equation with One Variable
The goal of solving a linear equation is to find the value of the unknown variable (usually 'x'). This is done by isolating the variable on one side of the equation using inverse operations. Follow the steps below to see how it works.
Example: Solve for x in 3x + 5 = 14
4. Methods for Solving Systems of Linear Equations
Sometimes you need to solve two or more linear equations at the same time. This is called a "system of equations." The solution is the single (x, y) point where the lines intersect. There are three common algebraic methods to find this solution.