Step-by-step explanation:
to get the original slope, we need to bring the line equation to
y = ...
and the slope is the factor of x.
x + 3y = 27
3y = -x + 27
y = -1/3 x + 9
so, the original slope is -1/3.
the perpendicular slope turns this upside-down and flips the sign : 3/1 = 3.
as the slope is the ratio "y coordinate change / x coordinate change".
we can use the point-slope form for the new line equation :
y - y1 = m(x - x1)
with m being the slope, and (x1, y1) being a point on the line.
so,
y - 6 = 3(x - 1)
simplified that is
y - 6 = 3x - 3
y = 3x + 3
that is then the slope-intercept form (+3 being the interception point on the y-axis).
