To find the equation of the line in point-slope form, we first need to calculate the slope \( m \) of the line connecting the two points \( (6, 5) \) and \( (8, 2) \).
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points:
- \( (x_1, y_1) = (6, 5) \)
- \( (x_2, y_2) = (8, 2) \)
We calculate:
\[ m = \frac{2 - 5}{8 - 6} = \frac{-3}{2} \]
Now that we have the slope \( m = -\frac{3}{2} \), we can use one of the points to write the equation in point-slope form. We'll use the point \( (6, 5) \).
The point-slope form of a line is given by:
\[ y - y_1 = m(x - x_1) \]
Substituting \( m = -\frac{3}{2} \), \( x_1 = 6 \), and \( y_1 = 5 \):
\[ y - 5 = -\frac{3}{2}(x - 6) \]
So the equation of the line in point-slope form is:
\[ y - 5 = -\frac{3}{2}(x - 6) \]