# How do you write an equation in standard form for the horizontal and vertical line through (4,5)?

Jul 20, 2017

See a solution process below:

#### Explanation:

The equation for a horizontal line going through $\left(4 , 5\right)$ is:

$y = 5$ where for each and every value of $x$, $y = 5$

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 then write the equation above as:

$\textcolor{red}{0} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{5}$

The equation for a vertical line going through $\left(4 , 5\right)$ is:

$x = 4$ where for each and every value of $y$, $x = 4$

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 then write the equation above as:

$\textcolor{red}{1} x + \textcolor{b l u e}{0} y = \textcolor{g r e e n}{4}$