To find the rate of change represented by the data in the table, follow these steps:
1. Identify the initial and final values:
- For [tex]\( x \)[/tex]: The initial value is [tex]\(-9\)[/tex] and the final value is [tex]\(7\)[/tex].
- For [tex]\( y \)[/tex]: The initial value is [tex]\(4\)[/tex] and the final value is [tex]\(16\)[/tex].
2. Calculate the change in [tex]\( y \)[/tex]:
[tex]\[
\Delta y = y_{\text{final}} - y_{\text{initial}} = 16 - 4 = 12
\][/tex]
3. Calculate the change in [tex]\( x \)[/tex]:
[tex]\[
\Delta x = x_{\text{final}} - x_{\text{initial}} = 7 - (-9) = 7 + 9 = 16
\][/tex]
4. Compute the rate of change:
[tex]\[
\text{Rate of Change} = \frac{\Delta y}{\Delta x} = \frac{12}{16}
\][/tex]
5. Simplify the fraction:
[tex]\[
\frac{12}{16} = \frac{3}{4} = 0.75
\][/tex]
Thus, the rate of change represented by the data in the table is [tex]\(0.75\)[/tex].
