Question

What is the slope of the line given by the equation 2x + 3y = 6?

Answer 1

you have a choice
you can solve for \(y\) via
\[2x+3y=6\\
3y=-2x+6\\
y=-\frac{2}{3}x+2\] now it looks like \(y=mx+b\) with slope \(m\) i.e. the slope is \(-\frac{2}{3}\)

Answer 2

or you can remember that the slope of
\[ax+by=c\] is always
\[m=-\frac{a}{b}\]