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.

graph: balloon hat creations, x-axis (number of hats), y-axis (balloons remaining), line from (0,500) to (some x, 0)

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

□ positive slope
□ negative slope
□ constant slope
□ increasing function
□ decreasing function

Explanation:

1. Slope Sign: As the number of hats created (\(x\)) increases, the number of remaining balloons (\(y\)) decreases. This means the slope (\(m=\frac{\Delta y}{\Delta x}\)) is negative (since \(\Delta y\) is negative when \(\Delta x\) is positive).
2. Constant Slope: The graph is a straight line, so it has a constant slope (linear relationship).
3. Function Type: Since \(y\) decreases as \(x\) increases, the function is decreasing. A positive slope or increasing function would mean \(y\) increases with \(x\), which is not the case here.

Answer:

B. negative slope, C. constant slope, E. decreasing function