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Question 628304: Consider the line 8x-7y=-1, find the equation of the line that is parallel to this line and passes through the point (1,3). Find the equation of the line that is perpendicular to this line and passes through the point (1,3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Consider the line 8x-7y=-1, find the equation of the line that is parallel to this line and passes through the point (1,3). Find the equation of the line that is perpendicular to this line and passes through the point (1,3)
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Standard form of equation for a straight line: y=mx+b, m=slope, b=y-intercept
Original line:
8x-7y=-1
7y=8x+1
y=8x/7+1/7
slope=8/7
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Perpendicular line:
slope:-7/8 (negative reciprocal of slope of original line.
Equation: y=-7x/8+b
solving for b using given point (1,3)
3=-7*1/8+b
b=3+7/8=31/8
equation: y=-7x/8+31/8
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Parallel line:
slope: 8/7 (same as slope of original line)
Equation: y=8x/7+b
solving for b using given point (1,3)
3=8*1/7+b
b=3-8/7=13/7
equation: y=8x/7+13/7
see graph below as a visual check:
red line:original
blue line: parallel
green line: perpendicular
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