The point-slope form of a line's equation is given by the formula:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope of the line, and \((x_1, y_1)\) is a point on the line.
Given that the slope \( m = \frac{7}{10} \) and the point \((x_1, y_1) = (9, -3)\), we can substitute these values into the point-slope formula:
\[ y - (-3) = \frac{7}{10}(x - 9) \]
This simplifies to:
\[ y + 3 = \frac{7}{10}(x - 9) \]
Thus, the equation of the line in point-slope form is:
\[ y + 3 = \frac{7}{10}(x - 9) \]