How does a graph show solutions to a linear equation?

A graph shows solutions to a linear equation by representing all possible combinations of variables as points on a two-dimensional plane. Each point (x, y) on the graph corresponds to a solution of the equation, where the x-coordinate represents the independent variable and the y-coordinate represents the dependent variable. The line formed by connecting these points illustrates the relationship between the variables, with every point on the line satisfying the linear equation. Thus, any point on the line is a solution to the equation.