On a history test, students earn $p$ points for each multiple-choice question answered correctly and $q$ points for each essay question answered correctly. The total score for the test is 120 points. The relationship between the number of multiple-choice questions answered correctly ($m$) and the number of essay questions answered correctly ($e$) is represented by a line on a coordinate plane. This line passes through the points $(24,0)$ and $(0,15)$. What is the value of $p$?