The first thing I'd do is put this equation into standard slope - intercept form.
12x - 5y = 2 Subtract 12x from each side
-5y = -12x + 2 Divide each side by -5 to isolate the y
y = 12/5(x) - 2/5
The slope for this equation is 12/5, so we just take that and plug it into the slope - intercept equation with the given points (2, 3)
y = mx + b Fill in the variables
3 = 12/5(2) + b Simplify
3 = 24/5 + b Subtract 24/5 (or 4 4/5) from each side
-9/5 = b
Now we just fill in the correct variables (m and b) in the equation to have our final answer.
y = 12/5x - 9/5