How do you find a standard form equation for the line with y-intercept is 3 and slope is 1?

Jan 14, 2017

See the entire solution process below:

Explanation:

First, we have the necessary information to write the equation for the line in slope-intercept form.

The slope-intercept form of a linear equation is:

$y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and color(blue)(b is the y-intercept value.

Substituting the values from the problem gives:

$y = \textcolor{red}{1} x + \textcolor{b l u e}{3}$

$y = 1 x + 3$

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

$y - \textcolor{red}{x} = 1 x - \textcolor{red}{x} + 3$

$- 1 x + 1 y = 0 + 3$

$- 1 x + 1 y = 3$

$- 1 \left(- 1 x + 1 y\right) = - 1 \times 3$

$1 x - 1 y = - 3$

$\textcolor{red}{1} x - \textcolor{b l u e}{1} y = \textcolor{g r e e n}{- 3}$