y - 8 = 4/3*(x - 8) in standard form

I believe "standard form"  is this : Ax + By = C  ...   so we have.....

y - 8 = 4/3*(x - 8)     add 8 to both sides

y = (4/3)(x - 8) + 8     multiply both sides by 3

3y = 4(x - 8) + 24     

3y = 4x - 32 + 24

3y = 4x - 8

8 = 4x - 3y

4x - 3y  = 8

y - 8 = 4/3*(x - 8) in standard form

$$\small{\text{$
\begin{array}{rcll}
y - 8 &=& \frac{4}{3}\cdot (x - 8) \quad &| \quad +8\\\\
y &=& \frac{4}{3}\cdot (x - 8) +8\\\\
y &=& \frac{4}{3}\cdot x - \frac{4}{3}\cdot 8 +8\\\\
y &=& \frac{4}{3}\cdot x - \frac{4}{3}\cdot 8 +\frac{3}{3}\cdot8\\\\
y &=& \frac{4}{3}\cdot x - 4\cdot \frac{8}{3} +3\cdot\frac{8}{3}\\\\
y &=& \frac{4}{3}\cdot x - \frac{8}{3}\\\\
\end{array}
$}}$$