# Write an equation for a line where the x-intercept is -2 and the y-intercept is 1?

Apr 11, 2017

See the entire solution process below:

#### Explanation:

The x-intercept of -2 can be written as $\left(- 2 , 0\right)$

The y-intercept of 1 can be written as $\left(0 , 1\right)$

Knowing two points we can find the slope. 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:

$m = \frac{\textcolor{red}{1} - \textcolor{b l u e}{0}}{\textcolor{red}{0} - \textcolor{b l u e}{- 2}} = \frac{\textcolor{red}{1} - \textcolor{b l u e}{0}}{\textcolor{red}{0} + \textcolor{b l u e}{2}} = \frac{1}{2}$

We can now use the point-slope formula to find equations 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 $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the slope we calculated and the values from the second point gives:

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{\frac{1}{2}} \left(x - \textcolor{red}{0}\right)$

$y - \textcolor{red}{1} = \textcolor{b l u e}{\frac{1}{2}} x$

We can also substitute the slope we calculated and the values from the first point giving:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{1}{2}} \left(x - \textcolor{red}{- 2}\right)$

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{\frac{1}{2}} \left(x + \textcolor{red}{2}\right)$

We can solve this for $y$ to put it into 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.

$y - \textcolor{red}{0} = \left(\textcolor{b l u e}{\frac{1}{2}} \times x\right) + \left(\textcolor{b l u e}{\frac{1}{2}} \times \textcolor{red}{2}\right)$

$y - \textcolor{red}{0} = \frac{1}{2} x + 1$

$y = \textcolor{red}{\frac{1}{2}} x + \textcolor{b l u e}{1}$