$a,{\textstyle \phantom{\rule{0.278em}{0ex}}}b$ are coefficients associated with the $x,{\textstyle \phantom{\rule{0.278em}{0ex}}}y$ values.

$c$ is the constant.

For simplicity, graphing and related mathematics are done using the slope-intercept form as it is the most convenient. However, expect to see and use both forms of representation.