Question

What is the equation of a line perpendicular to the line y=(4/9)x-2 that passes through the point (4,3)?

Answer 1

y=(4/9)x-2
This is in slope intercept form (y=mx+b), where m is the slope. 
A perpendicular line will have the opposite reciprocal of the slope.
So if the slope here is 4/9, then the perpendicular line's slope will be -9/4.

Now that you have the slope (-9/4) and a point (4, 3), you can use the point-slope formula to find the equation.
y - y₁ = m(x - x₁)
y - 3 = (-9/4)(x - 4)
y - 3 = (-9/4)x + 9
y = (-9/4)x + 12

So the answer will be:
C. y= -(9/4)x+12