3x - 2y + 4 = 0
-2y = -3x - 4
y = 3/2x + 2...slope here is 3/2. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal of a number, flip the number and change the sign. So the slope we will need is -2/3 (see how I flipped 3/2, making it -2/3...and changed the sign, making it -2/3.)
y = mx + b
slope(m) = -2/3
(4,3)...x = 4 and y = 3
now sub and find b, the y int
3 = -2/3(4) + b
3 = -8/3 + b
3 + 8/3 = b
9/3 + 8/3 = b
17/3 = b
so ur perpendicular equation is : y = -2/3x + 17/3....or 2x + 3y = 17...or 2x + 3y - 17 = 0
If the path is 2 feet wide, you actually have 14 feet of length and 6 of width.
Multiply that together and he has 84 ft left
