# How do you graph the line that passes through the origin parallel to the line x+y=10?

May 29, 2017

See a solution process below:

#### Explanation:

The equation in the problem is in Standard Form for 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

The slope of an equation in standard form is: $m = - \frac{\textcolor{red}{A}}{\textcolor{b l u e}{B}}$

Therefore, $\textcolor{red}{1} x + \textcolor{b l u e}{1} y = \textcolor{g r e e n}{10}$ has slope:

$m = - \frac{\textcolor{red}{1}}{\textcolor{b l u e}{1}} = - 1$

A line parallel to this line will, by definition have the same slope.

We know the $y$ intercept is $0$ because the line passes through the origin therefore when $x = 0$, $y = 0$

We can use the slope-intercept formula to write and equation:

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 we calculated and the $y$-intercept from the point in the problem gives:

$y = \textcolor{red}{- 1} x + \textcolor{b l u e}{0}$

Or

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

We can also solve for the Standard Form:

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

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

Or

$x + y = 0$