8x - 9y = 1
Solve for y:
-9y = -8x + 1
y = 8/9 x - 1/9
The slope of the given line is 8/9, so the slope of the perpendicular is -9/8.
y = mx + b
y = -9/8 x + b
The perpendicular passes through (3, -4).
-4 = -9/8 * 3 + b
-4 = -27/8 + b
b = -32/8 + 27/8
b = -5/8
The equation in slope-intercept form is
y = -9/8 x - 5/8
Now we change the equation to standard form.
8y = -9x - 5
The equation in standard form is
9x + 8y = -5
