# How do you find a standard form equation for the line with m=-3, b=0?

Apr 26, 2017

See the solution process below:

#### Explanation:

FIrst, we can write this equation in the 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 $\textcolor{b l u e}{b}$ is the y-intercept value.

Substituting the slope and y-intercept from the problem gives:

$y = \textcolor{red}{- 3} x + \textcolor{b l u e}{0}$

We can now transform this equation into the Standard Form of a linear equation. 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

$3 x + y = 3 x + \textcolor{red}{- 3} x + \textcolor{b l u e}{0}$

$3 x + y = 0 + \textcolor{b l u e}{0}$

$\textcolor{red}{3} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{0}$