If a line has slope $m$, any perpendicular line has slope $-\frac{1}{m}$ (negative reciprocal).

After you know the slope, substitute the coordinates of $R$ into $y=mx+b$ to solve for $b$.

Enter the points $(-4,6)$, $(6,1)$, and $(2,-3)$.

Compute the slope with

$\frac{1-6}{6-(-4)}$

to verify it is $-\frac{1}{2}$.

Take the negative reciprocal of $-\frac{1}{2}$ to get the perpendicular slope, $2$.

Graph each answer choice and see which one passes through $(2,-3)$ and is perpendicular to the line through $(-4,6)$ and $(6,1)$. The correct equation is the one that satisfies both conditions.

From the graph, line $t$ passes through $(-4,6)$ and $(6,1)$. The slope is

A line perpendicular to slope $-\frac{1}{2}$ has slope $2$ (the negative reciprocal).

Using point $R(2,-3)$ in $y=mx+b$ with $m=2$:

With $m=2$ and $b=-7$, the boat’s path is