Enter the variables a, b, and y into the calculator below. The linear equation calculator will evaluate and solve for the missing variable x.

Linear Equation Formula

A linear equation is a term used in mathematics to describe a linear line in the form:

Where xn are variables, also known as indeterminates, and a and b are coefficients or constants. These constants can sometimes be considered parameters of the equation. That is since they do not vary, having known constants can produce a solid line when extrapolated across all x values.

It’s also possible to think of a linear equation as a linear polynomial over a field. The solution to that polynomial is such that the value of the equation is true or 0. When there is only one variable, such is the case with the linear equation y=mx+b. The solution to that equation yields coordinate points in the Cartesian plane. Since there are two variables in the equation, there are two solutions, which are equations to the x and y-intercept of that line.

Linear Equation Definition

A linear equation is a mathematical statement that represents a straight line on a graph. It consists of two variables, usually represented as x and y, and an equality sign. The equation follows the form ax + by = c, where a, b, and c are constants. The goal is to find the values of x and y that satisfy the equation.

Linear equations are important because they allow us to describe and analyze relationships between two variables straightforwardly. By graphing these equations, we can visually represent the relationship between the variables and understand their behavior.

How to find the unknown variable in a linear equation?

We will now go over an example of how to calculate the unknown variable in a linear equation.

  1. The first step is to set up your equation, for this we will assume the form of the equation to be y=ax+b, but in reality, the equation can have an infinite number of variables, such as y=ax+cz+b. In that case, you would need to know two known variables in order to find the missing value, but back on to our example.
  2. The next step is to find the known values. When looking at a line in the form y=ax+b, both a, b, and y are known. For this example, we will say the values are 1,2, and 3 respectively.
  3. Next, we must manipulate the equation in order to have x on one side. After some manipulation, we find that x=(y-b)/x.
  4. Finally, enter the known values into the equation to solve for x. x=(3-2)/1 = 1. Our unknown variable is 1.
  5. Analyze the results and apply them to additional problems.

It’s extremely clear that solving for an unknown variable in an equation is as simple as manipulating the equation so that the unknown variable is on one side, then entering the constants.


What is a linear equation?

A linear equation describes the solution for any point along a line. The linear equation is typically used to calculate the Y value given an X value along a line.