which represents a linear function?

Question

y = x^3
y = 2x^2
y = -4x + 5
y = -3^2 + 2

Answer 1

A linear function is one that can be expressed in the form \( y = mx + b \), where \( m \) and \( b \) are constants, and the graph of the function is a straight line.

Let's analyze the given equations:

1. \( y = x^3 \): This is a cubic function, not linear.
2. \( y = 2x^2 \): This is a quadratic function, not linear.
3. \( y = -4x + 5 \): This is in the form of a linear equation \( y = mx + b \) (with \( m = -4 \) and \( b = 5 \)).
4. \( y = -3^2 + 2 \): This simplifies to \( y = -9 + 2 = -7 \), which represents a constant function (not linear).

The only equation that represents a linear function is:

\( y = -4x + 5 \).