To find the equation of a line in slope-intercept form, we need to use the slope-intercept formula, which is:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Given that the slope \( m \) is \( \frac{2}{7} \) and the line passes through the point \( (7, 0) \), we can find the y-intercept \( b \) by substituting \( x = 7 \) and \( y = 0 \) into the equation and solving for \( b \).
Substituting into the equation:
\[ 0 = \frac{2}{7}(7) + b \]
Simplifying:
\[ 0 = 2 + b \]
Solving for \( b \):
\[ b = -2 \]
Now we can write the equation in slope-intercept form using the slope \( m = \frac{2}{7} \) and the y-intercept \( b = -2 \):
\[ y = \frac{2}{7}x - 2 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{2}{7}x - 2 \]