Question

drag the tiles to match the behavior of the graph of a function with the slope of its graph. negative slope zero slope positive slope behavior of graph slope increasing decreasing constant

Explanation:

• For an increasing graph of a function, as the independent variable (e.g., \(x\)) increases, the dependent variable (e.g., \(y\)) also increases. This corresponds to a positive slope (since the slope \(m=\frac{\Delta y}{\Delta x}\) and \(\Delta y\) and \(\Delta x\) have the same sign, resulting in a positive value).
• For a decreasing graph, as the independent variable increases, the dependent variable decreases. So \(\Delta y\) and \(\Delta x\) have opposite signs, leading to a negative slope.
• For a constant (horizontal) graph, the change in the dependent variable (\(\Delta y\)) is zero as the independent variable changes. Thus, the slope \(m = \frac{0}{\Delta x}=0\), which is a zero slope.

Answer:

Behavior of Graph	Slope
decreasing	negative slope
constant	zero slope