To find the rate of change of the linear function, we can use the formula for the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ \text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, the coordinates for point C are \(C(0, -1)\) and for point D are \(D(2, -11)\).
Substituting the points into the formula, we have:
\[ m = \frac{-11 - (-1)}{2 - 0} = \frac{-11 + 1}{2} = \frac{-10}{2} = -5 \]
So, the rate of change is \(-5\).
The initial value is the y-value of the point where the line begins, which is the y-coordinate of point C. Therefore, the initial value is \(-1\).
Complete the statements:
The rate of change is -5 and the initial value is -1.
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