Explanation:
we have
y = -3x + 7
in such a slope-intercept form the factor of x is the slope of the line.
the slope is the ratio of
y coordinate change / x coordinate change
when going from one point on the line to another.
in our case that is -3 = -3/1 (as ratio).
a perpendicular slope (90°) is turning the original slope ratio upside-down and flips the sign.
so, the desired new slope is 1/3.
to get the new constant term (b) for our line, we use the slope and the coordinates of the given point :
5 = (1/3)×3 + b = 1 + b
b = 4
so, our desired equation is
y = (1/3)x + 4