SOLUTION: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. Contains the point (-7, 2) and is perpendicular to the line 3x &#

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Question 457364: Write the equation of the line that satisfies the given conditions. Express the final equation in standard form.
Contains the point (-7, 2) and is perpendicular to the line 3x − y = 4

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

the point (-7, 2)
3x+%26%238722%3B+y+=+4+.......->......3x+%26%238722%3B+4+=+y+

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 3, 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%283%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F3%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%2F3 Multiply the fractions.


So the perpendicular slope is -1%2F3



So now we know the slope of the unknown line is -1%2F3 (its the negative reciprocal of 3 from the line y=3%2Ax-4). Also since the unknown line goes through (-7,2), 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-2=%28-1%2F3%29%2A%28x%2B7%29 Plug in m=-1%2F3, x%5B1%5D=-7, and y%5B1%5D=2



y-2=%28-1%2F3%29%2Ax%2B%281%2F3%29%28-7%29 Distribute -1%2F3



y-2=%28-1%2F3%29%2Ax-7%2F3 Multiply



y=%28-1%2F3%29%2Ax-7%2F3%2B2Add 2 to both sides to isolate y

y=%28-1%2F3%29%2Ax-7%2F3%2B6%2F3 Make into equivalent fractions with equal denominators



y=%28-1%2F3%29%2Ax-1%2F3 Combine the fractions



y=%28-1%2F3%29%2Ax-1%2F3 Reduce any fractions

So the equation of the line that is perpendicular to y=3%2Ax-4 and goes through (-7,2) is y=%28-1%2F3%29%2Ax-1%2F3


So here are the graphs of the equations y=3%2Ax-4 and y=%28-1%2F3%29%2Ax-1%2F3




graph of the given equation y=3%2Ax-4 (red) and graph of the line y=%28-1%2F3%29%2Ax-1%2F3(green) that is perpendicular to the given graph and goes through (-7,2)