Two-variable linear equations and their graphs | Algebra I | Khan Academy

Introduction to Linear Equations00:00:00

A linear equation is an equation whose graph is a straight line. For example, y = 2x - 3 is a linear equation. When you plot the (x, y) pairs that satisfy this equation, you get a line.

Different Forms of Linear Equations00:04:25

Linear equations can also be written in other forms, such as 4x - 3y = 12. To graph this, find the intercepts: if x = 0, y = -4 (point 0,-4); if y = 0, x = 3 (point 3,0). Connecting these two points will define the line.

Non-Linear Equations00:06:04

Not all equations are linear. Examples of non-linear equations include y = x², x * y = 12, or 5/x + y = 10. These equations do not produce a straight line when graphed.

Definition of a Linear Equation00:07:03

A linear equation is an equation where every term is either a constant or a constant multiplied by a variable raised to the first power. Variables cannot be multiplied together, raised to powers other than one, or be in the denominator of a fraction.

Graphing a Linear Equation00:00:48

To graph a linear equation, pick some x values and calculate the corresponding y values. For y = 2x - 3, when x = 0, y = -3; when x = 1, y = -1; and when x = 2, y = 1. Plotting these points (0,-3), (1,-1), and (2,1) and connecting them forms a straight line.

Understanding Solutions of a Linear Equation00:02:24

Any (x, y) pair that satisfies the equation will lie on the line. Conversely, any point on the line represents a solution to the linear equation. For example, the point (-0.5, -4) is on the line y = 2x - 3, which can be verified by plugging the values into the equation.