To find the rate of change in the graph defined by the points (0, 5), (1, 7), (2, 9), (3, 11), and (4, 13), you can calculate the slope of the line connecting these points.
The slope (rate of change) between any two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's calculate the slope using the first two points \((0, 5)\) and \((1, 7)\):
\[ \text{slope} = \frac{7 - 5}{1 - 0} = \frac{2}{1} = 2 \]
You can also check using any other pair of points, and you’ll find that the slope remains consistent at 2.
Therefore, the rate of change in the graph is 2.