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?

Typically when changing from the the $y = mx+b$ form (slope-intercept form)  to the $ax+by=c$ form (standard form) you want $a$ and $b$ to be integers. First we can multiply both sides by three (because this is the denominator of the slope $m$), then just move the term with $x$ to the other side of the equation by adding $x$ to both sides:
$$\begin{align}
  y&=-\frac{1}{3}x+\frac{29}{3}\\
  3(y)&=3\left(-\frac{1}{3}x+\frac{29}{3}\right)\\
  3y&=-x+29\\\\
  x + 3y &= 29
\end{align}$$
More generally, if you wanted $a$,$b$, and $c$ to be integers in the standard form, you would first have to take the denominators of $m$ and $b$ from the slope-intercept form and multiply through by their least common multiple (in our case here, that least common multiple happens to just be $3$).
