# How do you write the standard form of the equation given (1,2) and slope 7?

Feb 12, 2017

$\textcolor{red}{7} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{5}$

#### Explanation:

First, we can write the 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 values from the problem gives:

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{7} \left(x - \textcolor{red}{1}\right)$

Now, we need to convert to standard form. 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 convert as follows:

$y - \textcolor{red}{2} = \left(\textcolor{b l u e}{7} \times x\right) - \left(\textcolor{b l u e}{7} \times \textcolor{red}{1}\right)$

$y - \textcolor{red}{2} = 7 x - 7$

$- \textcolor{b l u e}{7 x} + y - \textcolor{red}{2} + 2 = - \textcolor{b l u e}{7 x} + 7 x - 7 + 2$

$- 7 x + y - 0 = 0 - 5$

$- 7 x + y = - 5$

$- 1 \left(- 7 x + y\right) = - 1 \times - 5$

$\left(- 1 \times - 7 x\right) + \left(- 1 \times y\right) = 5$

$\textcolor{red}{7} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{5}$