Line Integrals Across Line Segment

Hello all,

I have a problem where I need to parametrize a line segment in order to evaluate a line integral, but I don't know how to do that. The problem is as follows:

"Evaluate $\displaystyle \int_C$ $\displaystyle ye^x ds$, where $\displaystyle C$ is the line segment joining $\displaystyle (1,2)$ to $\displaystyle (4,7)$."

The book has a small example about the parametrization of line segments, but I can't follow it. Can anyone give a blow-by-blow description of how to use the equation: $\displaystyle r(t) = (1-t)r_0 + tr_1 $ where $\displaystyle 0<t<1$?

I understand that $\displaystyle r_0 $ and $\displaystyle r_1 $ are just the two points, initial and final, but how do you plug them into the previous formula to get $\displaystyle x = [something]$ and $\displaystyle y = [something else]$?

Thanks for your consideration,

Austin Martin