Question

a balloon artist creates balloon hats for children at a stores grand opening. the graph shows the number of balloons the artist has remaining, y, after creating x hats.

balloon hat creations

what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created? choose three correct answers.

increasing function
positive slope
constant slope
negative slope
decreasing function

Explanation:

1. Constant Slope: The graph is a straight line, and all straight lines have a constant slope (the rate of change is uniform).
2. Negative Slope: As the number of hats created (\(x\)) increases, the number of balloons remaining (\(y\)) decreases. This means the line is decreasing from left to right, indicating a negative slope.
3. Decreasing Function: A function is decreasing when, as the input (\(x\), number of hats) increases, the output (\(y\), number of balloons remaining) decreases. This matches the relationship shown in the graph.

The "increasing function" and "positive slope" are incorrect because the \(y\)-value (balloons remaining) decreases as \(x\) (hats created) increases, so the function is decreasing, not increasing, and the slope is negative, not positive.

Answer:

• constant slope
• negative slope
• decreasing function