Answer
$y=x-1$ or, in general form, $x-y-1=0$
Work Step by Step
Through $(-1,-2)$ and $(4,3)$
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.
Two point through which the line passes are given. Use them to find the slope of the line:
$m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}=\dfrac{3-(-2)}{4-(-1)}=\dfrac{5}{5}=1$
Substitute $m$ and whichever of the given points into the formula and simplify to obtain the equation of this line:
$y-y_{1}=m(x-x_{1})$
$y-3=(1)(x-4)$
$y-3=x-4$
$y=x-4+3$
$y=x-1$ or, in general form, $x-y-1=0$
