Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 32

Determine an equation for the line that is shown below:


a.) Write the equation in slope intercept form.
b.) Write the equation in standard form


a.) The line passes through the points $(2, 0)$ and $(0,2)$. Then by using two point form, we have

$\begin{equation} \begin{aligned} y - y_1 &= \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)\\ \\ y - 0 &= \frac{2 - 0}{0 - 2} (x - 2)\\ \\ y &= \frac{2}{-2} (x - 2)\\ \\ y &= -(x - 2) \end{aligned} \end{equation}$

So, the equation in slope intercept form is
$y = -x + 2$

b.) Thus, the equation of the line in general form $Ax + By = C$, we get
$x +y = 2$