SOLUTION: Write the standard form of the equation of the line described. Please show work. through: (3, 4), perpendicular to y = - 3 x + 4

Algebra ->  Linear-equations -> SOLUTION: Write the standard form of the equation of the line described. Please show work. through: (3, 4), perpendicular to y = - 3 x + 4      Log On


   

Question 1009720: Write the standard form of the equation of the line described. Please show work.

through: (3, 4), perpendicular to y = - 3 x + 4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

through: (3, 4), perpendicular to y+=+-3x+%2B+4

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%28-3%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%2F-3%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%2B4). Also since the unknown line goes through (3,4), 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-4=%281%2F3%29%2A%28x-3%29 Plug in m=1%2F3, x%5B1%5D=3, and y%5B1%5D=4



y-4=%281%2F3%29%2Ax-%281%2F3%29%283%29 Distribute 1%2F3



y-4=%281%2F3%29%2Ax-3%2F3 Multiply



y=%281%2F3%29%2Ax-3%2F3%2B4Add 4 to both sides to isolate y

y=%281%2F3%29%2Ax-3%2F3%2B12%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B9%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B3 Reduce any fractions

So the equation of the line that is perpendicular to y=-3%2Ax%2B4 and goes through (3,4) is y=%281%2F3%29%2Ax%2B3


So here are the graphs of the equations y=-3%2Ax%2B4 and y=%281%2F3%29%2Ax%2B3




graph of the given equation y=-3%2Ax%2B4 (red) and graph of the line y=%281%2F3%29%2Ax%2B3(green) that is perpendicular to the given graph and goes through (3,4)




The standard form of a linear equation is Ax+%2B+Bx+=+C, where A, B, and C are constants.
so, the standard form of the equation in your case is:
-%281%2F3%29x+%2By=3