Answer:
y=-2x/3
Explanation:
Perpendicular lines have opposite reciprocal slopes.
An example of opposite reciprocals: -1/2 and 2
-1*2=-2
The reciprocal of -2 is -1/2.
In order to solve for slope, isolate y:
3x - 2y = 7 ==> solve for y
3x = 7 + 2y ==> add 2y on both sides to make y positive
3x - 7 = 2y ==> isolate y by subtracting 7 on both sides
y = (3x - 7)/2 ==> divide both sides by 2 in order to isolate y
y = 3x/2 - 7/2 ==> distribution
Hence, the slope is 3/2 <== 3x/2.
Now, find the perpendicular slope:
-1*3/2=-3/2
The reciprocal of -3/2 is -2/3 ==> the slope of the perpendicular equation
Now, find the equation of the line that passes through (3, -2):
y=mx+b ==> slope-intercept equation
-2=-2/3 * (3) + b ==> plugin (x=3, y=-2) and m=-2/3 which is the slope.
-2 = 3 * (-2/3) + b ==> solve for b
-2 = -6/3 + b
-2 = -2 + b
b = 0 ==> -2 + 0 = -2
y=-2x/3+0 ==> plugin the slope -2/3 and b=0.
y=-2x/3+0 ==> y=-2x/3
Hence, the equation is y=-2x/3.