To find the slope of the trend line that passes through the points [tex]\((1, 3)\)[/tex] and [tex]\((10, 25)\)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the points [tex]\((1, 3)\)[/tex] and [tex]\((10, 25)\)[/tex], we identify the coordinates as follows:
- [tex]\((x_1, y_1) = (1, 3)\)[/tex]
- [tex]\((x_2, y_2) = (10, 25)\)[/tex]
Now, we plug these coordinates into the slope formula:
1. Calculate the change in [tex]\(y\)[/tex] (the difference between [tex]\(y_2\)[/tex] and [tex]\(y_1\)[/tex]):
[tex]\[ y_2 - y_1 = 25 - 3 = 22 \][/tex]
2. Calculate the change in [tex]\(x\)[/tex] (the difference between [tex]\(x_2\)[/tex] and [tex]\(x_1\)[/tex]):
[tex]\[ x_2 - x_1 = 10 - 1 = 9 \][/tex]
3. Divide the change in [tex]\(y\)[/tex] by the change in [tex]\(x\)[/tex] to find the slope:
[tex]\[ \text{slope} = \frac{22}{9} \][/tex]
Therefore, the slope of the trend line that passes through the points [tex]\((1, 3)\)[/tex] and [tex]\((10, 25)\)[/tex] is [tex]\(\frac{22}{9}\)[/tex].
So, the correct answer is [tex]\(\boxed{\frac{22}{9}}\)[/tex].
