SOLUTION: Find the equation of the line passing through the point P(1, - 5) and perpendicular to the line 3x – 6y = 7. Write the equation in slope-intercept form.

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line passing through the point P(1, - 5) and perpendicular to the line 3x – 6y = 7. Write the equation in slope-intercept form.       Log On


   

Question 1078901: Find the equation of the line passing through the point P(1, - 5) and perpendicular to the line 3x – 6y = 7. Write the equation in slope-intercept form.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the line passing through the point P(1, -5) and
perpendicular to the line 3x+%96+6y+=+7=>3x+%96+7+=+6y=>%283%2F6%29x+%96+7%2F6+=+y=>y=%281%2F2%29x+%96+7%2F6+

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 1%2F2, 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%281%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%2F1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-2%2F1 Multiply the fractions.


So the perpendicular slope is -2



So now we know the slope of the unknown line is -2 (its the negative reciprocal of 1%2F2 from the line y=%281%2F2%29%2Ax-7%2F6). Also since the unknown line goes through (1,-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%2B5=-2%2A%28x-1%29 Plug in m=-2, x%5B1%5D=1, and y%5B1%5D=-5



y%2B5=-2%2Ax%2B%282%29%281%29 Distribute -2



y%2B5=-2%2Ax%2B2 Multiply



y=-2%2Ax%2B2-5Subtract -5 from both sides to isolate y

y=-2%2Ax-3 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F2%29%2Ax-7%2F6 and goes through (1,-5) is y=-2%2Ax-3


So here are the graphs of the equations y=%281%2F2%29%2Ax-7%2F6 and y=-2%2Ax-3




graph of the given equation y=%281%2F2%29%2Ax-7%2F6 (red) and graph of the line y=-2%2Ax-3(green) that is perpendicular to the given graph and goes through (1,-5)