Linear Equation Point Checker

Instantly verify if a given point lies on the line defined by a linear equation of the form Ax + By = C. Just enter your equation and point, and we'll do the rest!

Enter Equation (Ax + By = C):

Equation of the line. Make sure to include '=', e.g., 'x - 2y = 5'.

Enter Point (x, y):

Coordinates of the point to check. Use parentheses and comma, e.g., '(3, -4)'.

Visual Representation

Understanding Linear Equations and Point Checks

A linear equation in two variables (x and y) represents a straight line on a graph. The standard form is Ax + By = C, where A, B, and C are constants. Each point (x, y) on the line satisfies this equation.

To check if a point lies on a line, we substitute the x and y coordinates of the point into the equation. If the equation holds true (i.e., the left side equals the right side), then the point lies on the line. Otherwise, it does not.

For example, consider the equation 2x + y = 5 and the point (2, 1). Substituting x = 2 and y = 1 into the equation gives 2(2) + 1 = 5, which simplifies to 5 = 5. Since the equation is true, the point (2, 1) lies on the line 2x + y = 5.

This tool helps you quickly verify such relationships and provides a visual representation to enhance understanding.