Lesson 1: Graphing Linear Equations

Property

The graph of a linear equation $Ax + By = C$ is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.

Examples

• Is the point $(2, 7)$ a solution to the equation $y = 3x + 1$? Yes, because substituting the values gives $7 = 3(2) + 1$, which simplifies to $7 = 7$. The point is on the line.

• Is the point $(1, 3)$ a solution to the equation $y = 3x + 1$? No, because substituting the values gives $3 = 3(1) + 1$, which simplifies to $3 = 4$. This is false, so the point is not on the line.