Questions: Find the rate of change of the linear function shown in the graph. Then find the initial value. The rate of change is (Simplify your answer.)

Solution Steps

From the graph, identify two points that the line passes through. For example, let's choose the points (0, -2) and (2, 2).

The rate of change (slope) of a linear function is calculated using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, -2) and (2, 2): \[ \text{slope} = \frac{2 - (-2)}{2 - 0} = \frac{2 + 2}{2} = \frac{4}{2} = 2 \]

The initial value (y-intercept) is the y-coordinate of the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at (0, -2).

Final Answer