To determine the rate of change, often referred to as the slope, of the linear relationship modeled in the table, we can use any two points from the table and apply the slope formula. Here, we will use the first two points [tex]\((x_1, y_1) = (1, 2)\)[/tex] and [tex]\((x_2, y_2) = (3, 5)\)[/tex].
The formula to calculate the rate of change (slope) between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substitute the coordinates of the first two points into the formula:
[tex]\[
\text{slope} = \frac{5 - 2}{3 - 1}
\][/tex]
Perform the subtraction in both the numerator and the denominator:
[tex]\[
\text{slope} = \frac{3}{2}
\][/tex]
Thus, the rate of change of the linear relationship modeled in the table is [tex]\(\frac{3}{2}\)[/tex].
The correct answer is [tex]\(\frac{3}{2}\)[/tex].
