A map of the town that Hannah lives in can be represented by the Cartesian plane. Hannah starts off at $(-4, 9)$ and walks 10 units to the left and 7 units down to get to her new location. Along what line could she have walked to get to the new location directly from her old location? Express your answer in the form $ax+by=c$ where $c$ is a positive integer and $a$ and $b$ are integers not having any common factors other than 1.