Identifying Linear Functions - Equations

A linear function is a function that can be graphically represented as a straight line. It has the form $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

A non-linear function is a function that does not form a straight line when graphed. Its equation may involve exponents, roots, or other operations that create curves.

Non-Linear

Linear

Linear

Linear

Non-Linear

The slope $$m$$ represents the rate of change of the function, indicating how much $$y$$ changes for a unit change in $$x$$ .

The y-intercept $$b$$ is the point where the line crosses the y-axis, indicating the value of $$y$$ when $$x = 0$$ .

A function is linear if it can be expressed in the form $$y = mx + b$$ , where $$m$$ and $$b$$ are constants, and the highest power of $$x$$ is 1.