SOLUTION: The lines represented by the equations y+1/2x=4 and 3x+6y=12 are parallel, perpendicular or neither? Explain your reasoning.

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Question 383794: The lines represented by the equations y+1/2x=4 and 3x+6y=12 are parallel, perpendicular or neither? Explain your reasoning.
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


We know that parallel lines have equal slopes and perpendicular lines have slopes that are negative reciprocals. Put both of your equations into slope intercept form. Then by inspection of the coefficient on in each equation determine the slope, , of the graph of each equation.

If then the lines are parallel.

If where , then the lines are perpendicular. Or if one of the slopes is zero and the other is undefined, then the lines are also perpendicular.

Otherwise the lines are neither parallel nor perpendicular.

John

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Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find the slope of the 2 lines.
To do that, put the equations in slope-intercept form (that means solve for y).
The slope, m, is the coefficient of x in slope-intercept form.
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If the slopes are equal, they're parallel.
If the slopes are negative inverses, they're perpendicular.
If neither, they're neither.
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