Explanation:
the standard slope-intercept form is
y = ax + b
the factor of x (here "a") is always the slope of the line. b is the y-intercept (the y value when x = 0).
the slope of the other line is 5/6.
ok.
perpendicular to this means in a right angle (90°).
and that means that the fraction of "y coordinate change / x coordinate change" turns upside-down, and the sign has to flip.
so, the slope of our line is then -6/5.
and b ?
we use the given point.
1 = -6/5 × -9 + b = 54/5 + b
5/5 = 54/5 + b
b = -49/5
and our line equation is
y = (-6/5)x - 49/5