Answer
$y=-x-3.$
Work Step by Step
We know that by the Slope Formula: if $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ are on a line, then the slope is: $m=\frac{y_2-y_1}{x_2-x_1}$.
Hence here: $m=\frac{1-(-6)}{-4-3}=\frac{7}{-7}=-1.$
We know that if the slope of a line is $m$ and it contains $P_1(x_1,y_1)$, then its equation is: $y-y_1=m(x-x_1).$
Hence here: $y-1=-1(x-(-4))\\y-1=-(x+4)\\y-1=-x-4\\y=-x-3.$