To determine the slope of a trend line that passes through the points \((1,3)\) and \((10,25)\), we can use the slope formula. The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here are the steps to find the slope:
1. Identify the coordinates of the two points: \((x_1, y_1) = (1, 3)\) and \((x_2, y_2) = (10, 25)\).
2. Substitute these coordinates into the slope formula:
[tex]\[ m = \frac{25 - 3}{10 - 1} \][/tex]
3. Simplify the expression:
[tex]\[ m = \frac{22}{9} \][/tex]
Therefore, the slope of the trend line that passes through the points \((1, 3)\) and \((10, 25)\) is \(\frac{22}{9}\).
Comparing this result with the given options:
- \( -\frac{15}{2} \)
- \( -\frac{1}{2} \)
- \( \frac{2 \rho}{9} \)
- \( \frac{24}{7} \)
None of these match with [tex]\(\frac{22}{9}\)[/tex]. This suggests that there is no correct option provided among the given choices.
