# How do you write the standard form of the equation given (3,5) and slope 5/3?

Mar 20, 2017

$5 x - 3 y = 0$

#### Explanation:

Start with the slope-point form: $\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$
with the point $\left(\textcolor{red}{3} , \textcolor{b l u e}{5}\right)$ and slope $\textcolor{g r e e n}{\frac{5}{3}}$ to get:
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{5} = \textcolor{g r e e n}{\frac{5}{3}} \left(x - \textcolor{red}{3}\right)$

Our target form is the standard form: $A x + B y = C$

Multiplying both sides of our slope-point form by $3$
and expanding the left side:
$\textcolor{w h i t e}{\text{XXX}} 3 y \cancel{- 15} = 5 x \cancel{- 15}$

Re-arrange into standard form:
$\textcolor{w h i t e}{\text{XXX}} 5 x - 3 y = 0$