Given points P(-3,4) and Q(4,y) in a coordinate plane, for what value y of is the slope of the line through P and Q equal to 1/7?
The slope of two points is $\frac{y_1-y_2}{x_1-x_2}$. In order for the slope to be $\frac{1}{7}$, this equation has to equal $\frac{1}{7}$.
Plugging in values gives $\frac{4-y}{-3-4} = \frac{1}{7}$. Solving this equation gives $y = \boxed{5}$.