To find the equation of the line in point-slope form, we first need to determine the slope of the line that passes through the points (3, 2) and (6, 10).
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((3, 2)\) and \((6, 10)\), we can assign:
- \( (x_1, y_1) = (3, 2) \)
- \( (x_2, y_2) = (6, 10) \)
Now we can calculate the slope \( m \):
\[ m = \frac{10 - 2}{6 - 3} = \frac{8}{3} \]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
We can use one of the points to write the equation. Let's use the point \((3, 2)\):
\[ y - 2 = \frac{8}{3}(x - 3) \]
Thus, the equation of the line in point-slope form is:
\[ y - 2 = \frac{8}{3}(x - 3) \]