SOLUTION: determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-4y=-5 8x+6y=-5

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To figure out if one line is parallel/perpendicular to another, we must compare the two slopes of the two lines


So let's solve for y


Start with the first equation


Subtract from both sides


Rearrange the equation


Divide both sides by


Break up the fraction


Reduce



So the equation is now in slope-intercept form () where the slope is and the y-intercept is



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Now let's solve for y


Start with the given equation


Subtract from both sides


Rearrange the equation


Divide both sides by


Break up the fraction


Reduce



So the equation is now in slope-intercept form () where the slope is and the y-intercept is



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From the two equations, we found the first slope was and the second slope was . Notice how the second slope is simply the negative reciprocal of the first slope. So this tells us that the two lines are perpendicular.



If you don't believe me, or you need more proof, here's visual proof


Graph of (red) and (green)