the lines 2x + 4y =8 and 2x-y= 12 are which of the following: parallel, perpendicular, horizontal, and vertical

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Hello there!  The most efficient way to tackle this problem is to rewrite each of them in slope-intercept form (solving for "y"). So 2x + 4y = 8 → y = -1/2x + 2 and 2x-y = 12 → y = 2x - 12.  The next thing you will need to do will be to identify the slope in each new equation. They are -1/2 and 2 respectively.  Recall what it takes to have each relationship among slope.  Which conditions exist here?  The slopes are actually opposite reciprocals of each other, so the two lines are perpendicular to each other.  Finally, if you have a graphic calculator you can graph the two equations on the same coordinate plane to visually see their relationship.  This will allow you to check your answer.  Happy problem solving