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
$9x + y = 13$