Explanation:
the slope (a) is always the factor of x in an equation
y = ax + b
it is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
a perpendicular slope now turns this ratio fraction upside-down and flips the sign.
so, the perpendicular slope of 5/3 is -3/5.
therefore, the last 2 answer options are out.
we have the equation
y = -3/5 x + b
now we use the coordinates of the given point to find b.
-2 = -3/5 × 5 + b = -3 + b
1 = b
so, the correct equation is
y = -3/5 + 1