Answer and Step-by-step explanation:
Lines that are parallel have the same slope, which is also the coefficient of the x in a slope-intercept form equation.
In this case, the slope is 3, so we want to find the equations with slope 3.
1) y = 5x - 2; clearly, the slope is 5, not 3, so this does not work.
2) y = -(1/3)x + 4; again, the slope is -1/3, not 3, so this doesn't work.
3) 2y = 6x - 4; if we divide both sides by 2, we get: y = 3x - 2; so, this does work.
4) 2y = 3x + 8; if we divide both sides by 2, we get: [tex]y=\frac{3}{2} x+4[/tex]; here, the slope is 3/2, not 3, so this doesn't work.
5) y - 3x = 8; if we add 3x to both sides, we get: y = 3x + 8. The slope is 3, so this does work.
Thus, the equations that are parallel are: 2y = 6x - 4 and y - 3x = 8.
Hope this helps!
