# How do you write the standard form of a line given (4, -8) and has a slope of 5/4?

Aug 18, 2017

See a solution process below:

#### Explanation:

The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

Where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Therefore we can write:

$\frac{5}{4} = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Or

$- \frac{5}{-} 4 = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

So $\textcolor{red}{A} = 5$ and $\textcolor{b l u e}{B} = - 4$

We can substitute this into the formula to give:

$\textcolor{red}{5} x + \textcolor{b l u e}{- 4} y = \textcolor{g r e e n}{C}$

$\textcolor{red}{5} x - \textcolor{b l u e}{4} y = \textcolor{g r e e n}{C}$

We can now substitute the values from the point in the problem for $x$ and $y$ and solve for $\textcolor{g r e e n}{C}$:

$\left(\textcolor{red}{5} \cdot 4\right) - \left(\textcolor{b l u e}{4} \cdot - 8\right) = \textcolor{g r e e n}{C}$

$20 - \left(- 32\right) = \textcolor{g r e e n}{C}$

$20 + 32 = \textcolor{g r e e n}{C}$

$52 = \textcolor{g r e e n}{C}$

Substituting this gives the result:

$\textcolor{red}{5} x - \textcolor{b l u e}{4} y = \textcolor{g r e e n}{52}$