To find the equation of the line in point-slope form that passes through the points \( (8, 10) \) and \( (13, 17) \), we first need to calculate the slope of the line.
The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in our points \( (8, 10) \) and \( (13, 17) \):
\[ m = \frac{17 - 10}{13 - 8} = \frac{7}{5} \]
Now that we have the slope, we can use the point-slope form equation, which is:
\[ y - y_1 = m(x - x_1) \]
We can use either point. Let's use the point \( (8, 10) \):
\[ y - 10 = \frac{7}{5}(x - 8) \]
Thus, the equation of the line in point-slope form is:
\[ y - 10 = \frac{7}{5}(x - 8) \]
Looking at the response options provided, the correct answer is:
y − 10 = 7/5(x − 8).