3x + 7y = 21
7y = -3x + 21
y = -3/7x + 3 ......the slope here is -3/7. 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 7/3 (see how I flipped -3/7 making it -7/3....and then changed the sign, making it 7/3)
y = mx + b
slope(m) = 7/3
(0,2)....x = 0 and y = 2
now we sub and find b, the y int
2 = 7/3(0) + b
2 = b
so ur perpendicular equation is : y = 7/3x + 2....but we need it in standard form
y = 7/3x + 2....subtract 7/3x from both sides
-7/3x + y = 2...multiply both sides by -3
7x - 3y = -6 <== ur perpendicular equation in standard form