SOLUTION: The lines px+4y-2=0 and 2x-y+p=0 are perpendicular. Find the value of p.

Question 154830: The lines px+4y-2=0 and 2x-y+p=0 are perpendicular. Find the value of p.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
If the lines are perpendicular, then their slopes are negative reciprocals.
Let's put the two equations into the slope-intercept form: y = mx+b
First equation:
Subtract px from both sides of the equation.
Add 2 to both sides.
Finally, divide both sides by 4.
Simplify.
Here, the slope is
Second equation:
Add y to both sides.
or
Here, the slope is
The negative reciprocal of 2 is and this should equal the slope of the first equation, , so...
Simplify and solve for p. Multiply both sides by -4.
Simplify.

Check, are the slopes negative reciprocals?
Substitute p = 2.
Simplify.
...and this is the negative reciprocal of 2.

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