Answer
$y=x+6$, or, in general form, $x-y+6=0$
Work Step by Step
Through $(1,7);$ parallel to the line passing through $(2,5)$ and $(-2,1)$
Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope.
A point through which the line passes and the fact that the line whose equation must be found is parallel to the line passing through $(2,5)$ and $(-2,1)$ is known.
Two points through which the line parallel to one whose equation must be found are known. Use them to find its slope:
$m=\dfrac{1-5}{-2-2}=\dfrac{-4}{-4}=1$
Parallel lines have the same slope. This means the slope of the line whose equation must be found is also $1$.
Substitute $(x_{1},y_{1})$ and $m$ into the point-slope form of the equation of a line formula and simplify to obtain the answer:
$y-y_{1}=m(x-x_{1})$
$y-7=(1)(x-1)$
$y-7=x-1$
$y=x-1+7$
$y=x+6$, or, in general form, $x-y+6=0$
