Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 30

Determine an equation for the line that goes through $(2,-5)$ and $(1,4)$

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

We are given $(x_1, y_1) = (2, -5)$ and $(x_2, y_2) = (1,4)$
a.) Then by using two point form, we have

$\begin{equation} \begin{aligned} y - y_1 &= \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)\\ \\ y -(-5) &= \frac{4 - (-5)}{1 - 2} (x - 2)\\ \\ y + 5 &= \frac{4 + 5 }{1 - 2} (x - 2)\\ \\ y + 5 &= \frac{9}{-1}(x -2)\\ \\ y + 5 &= -9x + 18 \end{aligned} \end{equation}$

So, the equation in slope intercept form is
$y = -9x + 13$

b.) Thus, the equation in general form $Ax + By = C$, we get
$9x + y = 13$