Answer
$y=x-1$
Work Step by Step
First, we find the slope.
To find the slope of the line passing through $(-1,-2)$ and $(4,3)$,
we use the slope formula: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$.
Plug in the given values of $x$ and $y$: $m=\frac{3-(-2)}{4-(-1)}$.
Simplify to arrive at the slope: $m=1$.
We plug in the slope and the values of $x$ and $y$ into the equation $y=mx+b$:
$3=1(4)+b$.
Solve for $b$: $3=b+4$
$b=-1$.
Plug in the values of $m$ and $b$ into the formula to find the equation of the line:
$y=x-1$.
