Question

Which equation represents a linear function?
y=x2-3, y=√×-3, y=x3-3, y=x-3

Answer 1

To determine which equation represents a linear function, we need to look for an equation of the form \(y = mx + b\), where \(m\) and \(b\) are constants and the variable \(x\) is raised to the first power.

Let's analyze the given equations:

1. \(y = x^2 - 3\): This is a quadratic function because the highest power of \(x\) is 2.
2. \(y = \sqrt{x} - 3\): This represents a square root function, which is not linear.
3. \(y = x^3 - 3\): This is a cubic function because the highest power of \(x\) is 3.
4. \(y = x - 3\): This is a linear function in the form \(y = mx + b\) where \(m=1\) and \(b=-3\).

Thus, the equation that represents a linear function is:

**\(y = x - 3\)**.