# How do you write an equation of a line going through (2,1) and (-2,-1)?

Mar 18, 2016

$y = \frac{1}{2} x$

#### Explanation:

Recall that the general equation for a line is:

$\textcolor{t e a l}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = m x + b \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where:
$y =$y-coordinate
$m =$slope
$x =$x-coordinate
$b =$y-intercept

Determining the Equation of the Line
$1$. Start by labelling the coordinates to either be coordinate $1$ or $2$.

Coordinate $1$: $\left(\textcolor{red}{{x}_{1}} , \textcolor{t e a l}{{y}_{1}}\right) = \left(\textcolor{red}{2} , \textcolor{t e a l}{1}\right)$

Coordinate $2$: $\left(\textcolor{b l u e}{{x}_{2}} , \textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{{y}_{2}}\right) = \left(\textcolor{b l u e}{- 2} , \textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{- 1}\right)$

$2$. Find the slope between the two coordinates using the formula, $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

$m = \frac{\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{{y}_{2}} - \textcolor{t e a l}{{y}_{1}}}{\textcolor{b l u e}{{x}_{2}} - \textcolor{red}{{x}_{1}}}$

$m = \frac{\textcolor{\mathrm{da} r k \mathmr{and} a n \ge}{- 1} - \textcolor{t e a l}{1}}{\textcolor{b l u e}{- 2} - \textcolor{red}{2}}$

$m = \frac{- 2}{- 4}$

$\textcolor{v i o \le t}{m = \frac{1}{2}}$

$3$. Find the value of the y-intercept by substituting the slope and either coordinate $1$ or $2$ into $y = m x + b$. In this case, we will use coordinate $1$.

$y = m x + b$

$\textcolor{t e a l}{1} = \textcolor{v i o \le t}{\frac{1}{2}} \left(\textcolor{red}{2}\right) + b$

$1 = 1 + b$

$b = 0$

$4$. Rewrite the equation.

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} y = \frac{1}{2} x \textcolor{w h i t e}{\frac{a}{a}} |}}}$