Question

Find the equation of the line passing through (-7,-9) and perpendicular to 8x-9y +2=0

Answer 1

8x - 9y + 2 = 0
-9y = -8x - 2
y = 8/9x + 2/9.....the slope here is 8/9. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So our perpendicular line will need a slope of -9/8 (see how I flipped the slope and changed the sign)

y = mx + b
slope(m) = -9/8
(-7,-9)...x = -7 and y = -9
now we sub and find b, the y int
-9 = (-9/8)(-7) + b
-9 = 63/8 + b
-9 - 63/8 = b
-72/8 - 63/8 = b
-135/8 = b

so ur perpendicular equation is : y = -9/8x - 135/8