To determine the rate of change between the given points, we need to follow a few steps carefully. Below is a detailed, step-by-step solution:
1. List the given points:
[tex]\[
(-2, 17), (-1, 13), (1, 5), (2, 1), (3, -3)
\][/tex]
2. Determine the change in [tex]\( x \)[/tex] and the change in [tex]\( y \)[/tex] between the first and last points:
- The [tex]\( x \)[/tex]-values are [tex]\( -2 \)[/tex] and [tex]\( 3 \)[/tex].
- The [tex]\( y \)[/tex]-values are [tex]\( 17 \)[/tex] and [tex]\( -3 \)[/tex].
3. Calculate the change in [tex]\( x \)[/tex] (Δx):
[tex]\[
\Delta x = x_{\text{last}} - x_{\text{first}} = 3 - (-2) = 3 + 2 = 5
\][/tex]
4. Calculate the change in [tex]\( y \)[/tex] (Δy):
[tex]\[
\Delta y = y_{\text{last}} - y_{\text{first}} = -3 - 17 = -20
\][/tex]
5. Calculate the rate of change:
The rate of change (or the slope) is found by dividing the change in [tex]\( y \)[/tex] by the change in [tex]\( x \)[/tex]:
[tex]\[
\text{Rate of change} = \frac{\Delta y}{\Delta x} = \frac{-20}{5} = -4.0
\][/tex]
6. Conclusion:
Thus, the rate of change between the given points is [tex]\( -4.0 \)[/tex].
