Answer
$x+y=6$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the different forms of linear equations to find the equation of the line with the following given characteristcs:
\begin{array}{l}\require{cancel}
\text{through } (2,4)
\\\text{m}=-1
.\end{array}
Use the properties of equality to express the equation in the standard form.
$\bf{\text{Solution Details:}}$
Let $x_1=2,$ $y_1=4,$ and $m=-1.$
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions is
\begin{array}{l}\require{cancel}
y-4=-1(x-2)
.\end{array}
Using the Distributive Property and 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}
y-4=-1(x)-1(-2)
\\\\
y-4=-x+2
\\\\
x+y=2+4
\\\\
x+y=6
.\end{array}
