# How do you write an equation of a line given (-2,0) and (0,6)?

##### 2 Answers
May 30, 2017

See a solution process below:

#### 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:

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

The point $\left(0 , 6\right)$ is also the $y$ intercept. Therefore we can use the slope-intercept formula to find an equation for the line. 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 gives:

$y = \textcolor{red}{3} x + \textcolor{b l u e}{6}$

May 30, 2017

$y = 3 x + 6$

#### Explanation:

First let's find the slope, $m$:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{6 - 0}{0 - \left(- 2\right)}$

$m = \frac{6}{2} = 3$

Now, let's use the point slope formula of a line:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

and plug in $m = 3$ and one of the given points:

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

$y = 3 x + 6$