Which graph has a rate of change of zero?

Question

On a coordinate plane, a vertical line is at x = 3.
On a coordinate plane, a horizontal line is at y = 3.
On a coordinate plane, a line with positive slope goes through (0, 0) and (1, 3).
On a coordinate plane, a line with negative slope goes through (negative 1, 3) and (0, 0).

Answer 1

The graph that has a rate of change of zero is the horizontal line at \( y = 3 \).

A rate of change of zero means that as you move along the x-axis, the y-value does not change; it remains constant. The horizontal line at \( y = 3 \) meets this criterion since for any x-value, y is always 3.

In contrast:

• The vertical line at \( x = 3 \) has an undefined slope (since you cannot divide by zero), and thus does not have a rate of change.
• The line with a positive slope will have a positive rate of change.
• The line with a negative slope will have a negative rate of change.

Therefore, the line that is horizontal at \( y = 3 \) is the only one with a rate of change of zero.