Answer
$y=-x+2$ or, in general form, $x+y-2=0$
Work Step by Step
Through $(-2,4);$ slope $-1$
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.
Both the point and the slope are given, just substitute them into the formula and simplify to obtain the equation of this line:
$y-y_{1}=m(x-x_{1})$
$y-4=-(x+2)$
$y-4=-x-2$
$y=-x-2+4$
$y=-x+2$ or, in general form, $x+y-2=0$
