Step-by-step explanation:
point-slope form is
y - y1 = a(x - x1)
with a being the slope, and (x1,y1) being a point on the line.
the general form is
y = ax + b
a is again the slope. and b is the y-intercept (the y value when x = 0).
the slope is the ratio "y coordinate change / x coordinate change".
so, we need to find the slope of the original line :
x - 7y - 9 = 0
x - 9 = 7y
y = 1/7 x - 9/7
so, the original slope is 1/7.
the perpendicular slope turns the original slope upside-down and flips the sign.
so, it is
-7/1 = -7
the point slope form is
y - -4 = -7(x - 6)
y + 4 = -7(x - 6)
for the standard form we only need to do the multiplications and transform the equation into the above form :
y + 4 = -7(x - 6)
y + 4 = -7x + 42
y = -7x + 38
