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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-> 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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You can put this solution on YOUR website! 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