Just by looking at y = −x 2 + 1, how do you know that it does not represent a line?

A) x is squared.

B) There is no constant term.

C) There is an increase of 1.

D) The coefficient is − 1.

A. X is squared.

A.) x is squared

To determine whether the equation y = -x^2 + 1 represents a line or not, we need to analyze its characteristics. Here's how you can identify that it does not represent a line:

A) The presence of a squared term (x^2) in the equation indicates it is a quadratic equation, not a linear equation. A linear equation only has x raised to the power of 1, not a higher power.

B) The absence of a constant term (a term without any variable, in this case, x) implies that the line does not intersect the y-axis at any specific point. In a linear equation, there must be a constant term to establish a y-intercept.

C) The statement about "an increase of 1" is not a deciding factor in determining if the equation represents a line or not. It is important to note that the equation describes the relationship between x and y, but the specific increase mentioned does not provide enough information to determine if it is a line.

D) The coefficient of -1 only indicates a reflection or a change in concavity for a quadratic equation. It does not alone determine whether the equation represents a line or not.

Therefore, the correct answer is B) There is no constant term. The absence of a constant term (like +c or +k) indicates that the equation does not represent a line, but rather a parabola in this particular case.