First let's put 3y = -4x + 2 into slope-intercept form. That way we can figure out the slope easier. Remember that slope-intercept from is: y = mx + b, where m = the slope and b = y-intercept.
To change 3y = -4x + 2 into that form, all we have to do is divide both sides by 3 to get y alone:
[tex]3y = -4x + 2 \\
y = - \frac{4}{3} x + \frac{2}{3} [/tex]
Since the "m" in slope-intercept form is the slope of the equation, that means [tex]- \frac{4}{3}
[/tex] is the slope of [tex]y = - \frac{4}{3} x + \frac{2}{3} [/tex].
As a general rule to find a slope that is perpendicular, just find the negative inverse/reciprocal of your slope, meaning flip numerator and denominator of your slope and multiply by -1. Since your slope is [tex]- \frac{4}{3} [/tex], the negative inverse/reciprocal of your slope (aka the perpendicular slope) would be: [tex]\frac{3}{4}[/tex].
The answer is A) 3/4.
