# How do you write the equation of a line given (6,-3),(-2,-3)?

Jun 7, 2017

$y = - 3$

#### Explanation:

First, we need to determine the slope of the line. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{- 3}}{\textcolor{red}{- 2} - \textcolor{b l u e}{6}} = \frac{\textcolor{red}{- 3} + \textcolor{b l u e}{3}}{\textcolor{red}{- 2} + \textcolor{b l u e}{- 6}} = \frac{0}{-} 8 = 0$

Next we can use the point-slope formula to write an equation for the line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through. Substituting the slope we calculated and the values from the second point in the problem gives:

$\left(y - \textcolor{red}{- 3}\right) = \textcolor{b l u e}{0} \left(x - \textcolor{red}{6}\right)$

$\left(y + \textcolor{red}{3}\right) = 0$

$y = - 3$

Jun 7, 2017

$y = - 3$

#### Explanation:

Begin by finding the slope using the slope formula:
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Let $\left(6 , - 3\right) \to \left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ and $\left(- 2 , - 3\right) \to \left(\textcolor{red}{{x}_{2}} , \textcolor{b l u e}{{y}_{2}}\right)$

Find the slope:

$m = \frac{\textcolor{b l u e}{- 3 - \left(- 3\right)}}{\textcolor{red}{- 2 - 6}} = \frac{0}{-} 8 = 0$

The equation of the line can be found using the point-slope formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is a point on the function. Since we have a slope and two points (we can choose either one. I will use $\left(- 2 , - 3\right)$), we can substitute this information like so:

$y - \left(- 3\right) = 0 \left(x - \left(- 2\right)\right)$

Simplify:

$y + 3 = 0 x + 0$

$y + 3 = 0$

Write in $y = m x + b$ form by isolating the $y$

$y + \cancel{3 - 3} = 0 - 3$

$y = - 3$ <-- Equation of the line

Jun 7, 2017

See a solution process below:

#### Explanation:

Because both of the $y$ values are the same and equal to $\textcolor{red}{- 3}$ we know, by definition this is a horizontal line.

Horizontal lines have the form:

$y = \textcolor{red}{a}$ where $a$ is the value of $y$ which is the same for each and every value of $x$.

Therefore, for this problem, an equation is:

$y = \textcolor{red}{- 3}$