Changing $y=mx+b$ equation into $ax+by=c$ I'm stuck on this question and I'm not totally sure how to transform an equation of the form $y=mx+b$ into an equation of the form $ax+by=c$. This is how far I have gotten 
$$y=-\frac{1}{3}x+\frac{29}{3}$$
How do I transform this into an $ax+by=c$ equation?

You transform it into
$$
\frac{1}{3} x + y = \frac{29}{3}
$$
by adding $(1/3) x$ to both sides of the equation. So you got $a = 1/3$ and $b = 1$ and $c = 29/3$.
In fact for $\lambda \ne 0$ the set of solutions $(x,y)$ does not change, if we multiply both sides by $\lambda$:
$$
\frac{\lambda}{3}x + \lambda y = \frac{29\lambda}{3}
$$
Among all those equations one can decide for a nice looking one, in this case $\lambda = 3$ looks a bit less complex (no division):
$$
x + 3y = 29
$$
