Explanation:
the slope of a line is always the factor of x, and it is defined as ratio (y coordinate change / x coordinate change) when going from one point to another on the line.
in that sense it is y/x.
the perpendicular slope turns that ratio upside-down and flips the overall sign.
so, in our case, the original slope is 3 = 3/1.
the perpendicular slope is then -1/3.
so, now, we have the slope and a point, and we can start with the point-slope form of the line equation :
y - y1 = a(x - x1)
"a" being the slope, (x1, y1) being the point.
y - 1 = -1/3 × (x - 9) = -x/3 + 3
y = -x/3 + 4
and that is the usual slope-intercept form
y = ax + b
"a" is again the slope, "b" is the y-intercept (the y value when x = 0).