The equation of this line is y = -5/2x - 1
In order to find this, we first need to solve the initial equation for slope intercept form. This way we can see the slope, which is essential for finding a parallel line.
5x + 2y = 12 -----> Subtract 5x
2y = -5x + 12 ----> Divide by 2
y = -5/2x + 6
Now we can tell the slope of our new line will be -5/2. This is because parallel lines have the same slope. We'll use that along with the included point to find the intercept of the new line.
y = mx + b
4 = (-5/2)(-2) + b
4 = 5 + b
-1 = b
Now we know the intercept and the slope, we can use those to model the equation.
y = -5/2x - 1