Question

which of the following graphs represent a linear function? select all that apply.

Explanation:

Step1: Recall linear function graph

A linear function has the form \( y = mx + b \), and its graph is a straight line (non - curved, constant slope).

Step2: Analyze each graph

• First graph (purple line): It is a straight line, so it represents a linear function.
• Second graph (green curve): It is a curved line, so it does not represent a linear function (it is a non - linear curve, likely a square - root or some other non - linear relation).
• Third graph (blue parabola): It is a parabola (the graph of a quadratic function \( y=ax^{2}+bx + c \)), which is a curved line, so it does not represent a linear function.
• Fourth graph (orange line): It is a horizontal straight line (which can be written as \( y = k\) where \(k\) is a constant, and in the form of \(y=mx + b\), \(m = 0\) and \(b=k\)), so it represents a linear function.

Answer:

The first graph (purple straight line) and the fourth graph (orange horizontal straight line) represent linear functions.