SOLUTION: Decide whether the pair of lines is parallel, perpendicular, or neither.
4x+3y=5
3x-4y=4
What is the slope of 4x+3y=5
What is the slope of 3x-4y=4
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Question 189713: Decide whether the pair of lines is parallel, perpendicular, or neither.
4x+3y=5
3x-4y=4
What is the slope of 4x+3y=5
What is the slope of 3x-4y=4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the first equation.
Subtract from both sides.
Rearrange the terms.
Divide both sides by to isolate y.
Break up the fraction.
Reduce.
So we can see that the equation has a slope and a y-intercept .
-------------------------------
Now move onto the second equation.
Subtract from both sides.
Rearrange the terms.
Divide both sides by to isolate y.
Break up the fraction.
Reduce.
So we can see that the equation has a slope and a y-intercept .
--------------------------------------
So the slope of the first line is and the slope of the second line is .
Notice how the slope of the second line is simply the negative reciprocal of the slope of the first line .
In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope. So this means that and are perpendicular lines.
So consequently, this also means that and are perpendicular lines.
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