Which statement best explains whether the equation y = 2x − 4 represents a linear or nonlinear function?

Question

Which statement best explains whether the equation y = 2x − 4 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because its graph contains the points (0, 2), (2, 3), and (4, 4), which are on a straight line.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (0, 2), (2, 3), and (4, 4), which are not on a straight line.

GPT-4o mini · Answer

The correct statement is: **The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.** Explanation: The equation $y = 2x - 4$ is in the standard form of a linear equation (y = mx + b), where $m$ is the slope and $b$ is the y-intercept. It represents a straight line when graphed, and both the independent variable $x$ and the dependent variable $y$ have an exponent of 1, which characterizes linear functions. The points mentioned in the other options do not accurately represent a straight line.