# How do you find a standard form equation for the line with slope -2/5 passing through the point (8,4)?

Mar 24, 2017

See the entire solution process below:

#### Explanation:

First, we can write an equation in point-slope form. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the slope and values from the point given in the problem gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- \frac{2}{5}} \left(x - \textcolor{red}{8}\right)$

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

We can solve for this form as follows:

First, multiple each side of the equation by $\textcolor{g r e e n}{5}$ to remove the fraction. In standard form both the coefficients and the constant must be integers:

$\textcolor{g r e e n}{5} \left(y - \textcolor{red}{4}\right) = \textcolor{g r e e n}{5} \times \textcolor{b l u e}{- \frac{2}{5}} \left(x - \textcolor{red}{8}\right)$

$\left(\textcolor{g r e e n}{5} \times y\right) - \left(\textcolor{g r e e n}{5} \times \textcolor{red}{4}\right) = \cancel{\textcolor{g r e e n}{5}} \times \textcolor{b l u e}{- \frac{2}{\cancel{5}}} \left(x - \textcolor{red}{8}\right)$

$5 y - 20 = - 2 \left(x - 8\right)$

Next, expand the terms on the right side of the equation:

$5 y - 20 = \left(- 2 \times x\right) - \left(- 2 \times 8\right)$

$5 y - 20 = - 2 x - \left(- 16\right)$

$5 y - 20 = - 2 x + 16$

Now, add $\textcolor{g r e e n}{20}$ and (color)(red)(2x) to each side of the equation to put this equation in Standard Form:

$\textcolor{red}{2 x} + 5 y - 20 + \textcolor{g r e e n}{20} = \textcolor{red}{2 x} - 2 x + 16 + \textcolor{g r e e n}{20}$

$\textcolor{red}{2 x} + 5 y - 0 = 0 + \textcolor{g r e e n}{36}$

$\textcolor{red}{2} x + \textcolor{b l u e}{5} y = \textcolor{g r e e n}{36}$