#### Answer

$x-3y=-7$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the Two-Point Form of linear equations to find the equation of the line with the following given characteristcs:
\begin{array}{l}\require{cancel}
\text{through }
(2,3)
\text{ and }
(-1,2)
.\end{array}
Use the properties of equality to express the equation in the standard form.
$\bf{\text{Solution Details:}}$
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form of linear equations, where
\begin{array}{l}\require{cancel}
x_1=2
,\\x_2=-1
,\\y_1=3
,\\y_2=2
,\end{array}
the equation of the line is
\begin{array}{l}\require{cancel}
y-3=\dfrac{3-2}{2-(-1)}(x-2)
\\\\
y-3=\dfrac{3-2}{2+1}(x-2)
\\\\
y-3=\dfrac{1}{3}(x-2)
.\end{array}
Using the properties of equality, in the form $ax+by=c$ or the Standard Form, the equation above is equivalent to
\begin{array}{l}\require{cancel}
3(y-3)=\left[ \dfrac{1}{3}(x-2) \right]3
\\\\
3(y-3)=1(x-2)
\\\\
3y-9=x-2
\\\\
-x+3y=-2+9
\\\\
-x+3y=7
\\\\
-1(-x+3y)=-1(7)
\\\\
x-3y=-7
.\end{array}