5y + 2x = 12
Let's put this equation in y intercept form, y = mx + b. Solve this equation for y. Start by subtracting 2x from both sides.
5y = 12 - 2x
Divide both sides by 5.
y = 12/5 - 2/5x
Parallel lines have the same slopes, so that means the line that is parallel to this line must have the same slope. The slope of this line is the coefficient of the variable x.
The slope of this line is -2/5, so the line that is parallel to this line must also have a slope of -2/5.
Your answer is A) -2/5.