Alright, let's solve this step-by-step.
We are given pairs of input and output values:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Input (x)} & \text{Output (y)} \\
\hline
1 & 11 \\
\hline
2 & 13 \\
\hline
3 & 15 \\
\hline
4 & 17 \\
\hline
5 & 19 \\
\hline
\end{array}
\][/tex]
We need to determine the rate of change for each consecutive pair of points. The rate of change can be found using the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
\text{Rate of change} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Let's compute this for each pair of consecutive points:
1. Between [tex]\((1, 11)\)[/tex] and [tex]\((2, 13)\)[/tex]:
[tex]\[
\text{Rate of change} = \frac{13 - 11}{2 - 1} = \frac{2}{1} = 2.0
\][/tex]
2. Between [tex]\((2, 13)\)[/tex] and [tex]\((3, 15)\)[/tex]:
[tex]\[
\text{Rate of change} = \frac{15 - 13}{3 - 2} = \frac{2}{1} = 2.0
\][/tex]
3. Between [tex]\((3, 15)\)[/tex] and [tex]\((4, 17)\)[/tex]:
[tex]\[
\text{Rate of change} = \frac{17 - 15}{4 - 3} = \frac{2}{1} = 2.0
\][/tex]
4. Between [tex]\((4, 17)\)[/tex] and [tex]\((5, 19)\)[/tex]:
[tex]\[
\text{Rate of change} = \frac{19 - 17}{5 - 4} = \frac{2}{1} = 2.0
\][/tex]
Summarizing, the rate of change between each consecutive pair of points is:
[tex]\[
[2.0, 2.0, 2.0, 2.0]
\][/tex]
Therefore, the rate of change is consistent and equal to 2.0 for each interval between the given points.
