# How do you write an equation in point slope and slope intercept form given (1, 0) and (0, 2)?

Jan 31, 2017

The point-slope forms are:

$\left(y - 0\right) = - 2 \left(x - 1\right)$ or $y = - 2 \left(x - 1\right)$

Or

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

The slope-intercept for is:

$y = - 2 x + 2$

#### Explanation:

First, we need to determine the slope of the line for the point-slope form and the slope intercept form. 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 points from the problem and calculating gives:

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

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 calculate and the first point from the problem gives:

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

We can also substitute the slope we calculate and the second point from the problem gives:

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

Because we have the slope and by definition the y-intercept is the point $\left(0 , 2\right)$ we can substitute this into the slope-intercept formula. 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.

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