Question

1. what is true about the graph of a linear function?

a. it has no slope.
b. it forms a curve.
c. it forms a straight line.
d. it passes through multiple y-values for each x.

Explanation:

To determine the correct answer, we analyze each option based on the definition of a linear function:

• Option a: A linear function has a constant slope (either positive, negative, zero, or undefined in the case of a vertical line, but vertical lines aren't functions). So it does have a slope, eliminating a.
• Option b: By definition, a linear function's graph is a straight line, not a curve. Curves are associated with non - linear functions (e.g., quadratic, exponential). So b is incorrect.
• Option c: The definition of a linear function (in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept) states that its graph is a straight line. This option is correct.
• Option d: A function, by definition, can only have one \(y\) - value for each \(x\) - value. So a linear function (which is a function) cannot pass through multiple \(y\) - values for each \(x\), eliminating d.

Answer:

c. It forms a straight line.