Question

Examine the graph of the function.

The graph of a line that contains points (negative 1, 7), (0, 5), and (2, 1).

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What is the rate of change of the function?

Enter your answer as a number, like this: 42

Answer 1

The rate of change of the function represented by the line containing points (negative 1, 7), (0, 5), and (2, 1) is -2. The slope was calculated using the formula Δy/Δx with the points (2, 1) and (-1, 7).

Step-by-step explanation:

To find the rate of change of the function represented by the graph of a line, we can use any two points on the line to calculate the slope.

The slope formula, which is the rate of change, is given by (change in y) / (change in x), or Δy/Δx. Let’s use the points (2, 1) and (-1, 7) for our calculation.

The change in y is 1 - 7 = -6 and the change in x is 2 - (-1) = 3.

So, the slope or rate of change is -6 / 3 = -2.

The negative sign indicates that the line is decreasing, meaning that as the x-value increases, the y-value decreases.