First you find the slope of the given line. The formula for slope for line in standard form (ax + by = c) is -a/b, so for this line the slope is -3/2.
A perpendicular line's slope is the negative reciprocal of the original line's slope. So the new line will have a slope of 2/3.
Now we can use the given point and the slope to calculate the y-intercept. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We sub in the given point to yield:
8 = (2/3)(3) + b
8 = 6 + b
b = 2
The line that is perpendicular to 3x + 2y = 10 and goes through point (3,8) is: y = (2/3)x + 6
Standard form answer: -2x + 3y = 18