Question

what is the rate of change of the function represented by this graph? graph with x-axis: number of items (0 - 12), y-axis: cost in dollars (1 - 7). points at (0,4), (4,5), (8,6), (12,7). multiple choice options: $0.25 per item, $25 per item, $4 per item, -$0.25 per item

Explanation:

Step1: Identify two points

From the graph, we can take two clear points. Let's use (0, 4) and (4, 5). The first point is when the number of items (x) is 0, cost (y) is 4. The second is when x = 4, y = 5.

Step2: Calculate rate of change

The rate of change (slope) of a linear function is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values: $y_2 = 5$, $y_1 = 4$, $x_2 = 4$, $x_1 = 0$. So $m=\frac{5 - 4}{4 - 0}=\frac{1}{4}=0.25$. This means the rate of change is $0.25 per item.

Answer:

$0.25 per item