The slope-intercept form of a line is given by the equation:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Given that the slope \( m \) is \( \frac{5}{7} \) and the y-intercept \( b \) is \( \frac{3}{7} \), we can substitute these values into the equation:
\[ y = \frac{5}{7}x + \frac{3}{7} \]
To express this in a form with integers, proper fractions, and improper fractions, we will leave it as is since both \( \frac{5}{7} \) and \( \frac{3}{7} \) are already in their simplest form and are proper fractions.
Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{5}{7}x + \frac{3}{7} \]