
Originally Posted by
MathTooHard
Given two points and the slope between them, you can write the line in point slope form: $\displaystyle y-y_1=m(x-x_1)$, where $\displaystyle m$ is the slope. The slope is rise over run, which is $\displaystyle \frac{8-5}{7-2}=\frac{3}{5}$. Now, we choose any given point and plug it into the equation. Let's choose $\displaystyle (2,5)$, and we get $\displaystyle y-5=\frac{3}{5}(x-2)$. From there you can manipulate the equation to standard form: $\displaystyle ax+by=c$, where $\displaystyle a, b, c$ are integers.