SOLUTION: Y=-6x+6 Find the equation of the line that is parallel to this line and passes through the point (7,5) Find the equation of the line that is perpendicular to this line and pa

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Question 769038: Y=-6x+6
Find the equation of the line that is parallel to this line and passes through the point (7,5)
Find the equation of the line that is perpendicular to this line and passes through the point(7,5)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the line that is parallel to this line and passes through the point (7,5):
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -6 (its from the slope of y=-6%2Ax%2B6 which is also -6). Also since the unknown line goes through (7,5), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-5=-6%2A%28x-7%29 Plug in m=-6, x%5B1%5D=7, and y%5B1%5D=5



y-5=-6%2Ax%2B%286%29%287%29 Distribute -6



y-5=-6%2Ax%2B42 Multiply



y=-6%2Ax%2B42%2B5Add 5 to both sides to isolate y

y=-6%2Ax%2B47 Combine like terms

So the equation of the line that is parallel to y=-6%2Ax%2B6 and goes through (7,5) is y=-6%2Ax%2B47


So here are the graphs of the equations y=-6%2Ax%2B6 and y=-6%2Ax%2B47



graph of the given equation y=-6%2Ax%2B6 (red) and graph of the line y=-6%2Ax%2B47(green) that is parallel to the given graph and goes through (7,5)





the equation of the line that is perpendicular to this line and passes through the point(7,5):
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of -6, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%28-6%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-6%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=1%2F6 Multiply the fractions.


So the perpendicular slope is 1%2F6



So now we know the slope of the unknown line is 1%2F6 (its the negative reciprocal of -6 from the line y=-6%2Ax%2B6). Also since the unknown line goes through (7,5), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-5=%281%2F6%29%2A%28x-7%29 Plug in m=1%2F6, x%5B1%5D=7, and y%5B1%5D=5



y-5=%281%2F6%29%2Ax-%281%2F6%29%287%29 Distribute 1%2F6



y-5=%281%2F6%29%2Ax-7%2F6 Multiply



y=%281%2F6%29%2Ax-7%2F6%2B5Add 5 to both sides to isolate y

y=%281%2F6%29%2Ax-7%2F6%2B30%2F6 Make into equivalent fractions with equal denominators



y=%281%2F6%29%2Ax%2B23%2F6 Combine the fractions



y=%281%2F6%29%2Ax%2B23%2F6 Reduce any fractions

So the equation of the line that is perpendicular to y=-6%2Ax%2B6 and goes through (7,5) is y=%281%2F6%29%2Ax%2B23%2F6


So here are the graphs of the equations y=-6%2Ax%2B6 and y=%281%2F6%29%2Ax%2B23%2F6




graph of the given equation y=-6%2Ax%2B6 (red) and graph of the line y=%281%2F6%29%2Ax%2B23%2F6(green) that is perpendicular to the given graph and goes through (7,5)