Question

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

Answer 1

the slope in the given equation, y = 4/9x - 2, is 4/9. However, we need the perpendicular slope, also called the negative reciprocal slope. All that means is " flip " the slope given and change the sign. So the negative reciprocal of 4/9 is -9/4. See how I flipped the slope and changed the sign.
Now we use y = mx + b
slope(m) = - 9/4
(4,3) x = 4 and y = 3
now we sub
y = mx + b
3 = -9/4(4) + b
3 = - 9 + b
3 + 9 = b
12 = b
Therefore, your perpendicular equation is : y = -9/4x + 12
any questions ?

Answer 2

I've got it now, thanks for the detailed explanation <3

Answer 3

no problem :)