Given that line $r$ is parallel to line $q$, they must have the same slope.

The slope of line $q$ is $\frac{2}{5}$. Since parallel lines have identical slopes, the slope of line $r$ is also $\frac{2}{5}$.

Thus, the slope of line $r$ is: $\frac{2}{5}$

Do you want more details or have any questions?

Here are 5 related questions to expand on this concept:

1. What is the slope of a line perpendicular to line $q$?
2. How do you calculate the slope of a line given two points on the line?
3. How do parallel and perpendicular lines behave differently in geometry?
4. Can two lines with different slopes ever be parallel?
5. How would you graph a line with a slope of $\frac{2}{5}$?

Tip: Parallel lines have identical slopes but different y-intercepts.