Find the equation of a line with the following information. Passes through (4,3) and is perpendicular to the straight line 3x-2y+4=0

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