SOLUTION: Find an equation for the linear function g(x) which is perpendicular to the line 3x−2y=6 and intersects the line 3x−2y=6 at x=8. g(x)=

Algebra ->  Rational-functions -> SOLUTION: Find an equation for the linear function g(x) which is perpendicular to the line 3x−2y=6 and intersects the line 3x−2y=6 at x=8. g(x)=       Log On


   

Question 906069: Find an equation for the linear function g(x) which is perpendicular to the line 3x−2y=6 and intersects the line 3x−2y=6 at x=8.
g(x)=
Found 2 solutions by MathLover1, lwsshak3:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
3x%26%238722%3B2y=6
the linear function g(x) which is perpendicular to 3x%26%238722%3B2y=6 and
intersection point at x=8: (8,+0+)
3x%26%238722%3B2y=6 ...first solve for y
3x%26%238722%3B6=2y
%283%2F2%29x%26%238722%3B3=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%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%283%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%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=-2%2F3 Multiply the fractions.


So the perpendicular slope is -2%2F3



So now we know the slope of the unknown line is -2%2F3 (its the negative reciprocal of 3%2F2 from the line y=%283%2F2%29%2Ax-3). Also since the unknown line goes through (8,0), 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-0=%28-2%2F3%29%2A%28x-8%29 Plug in m=-2%2F3, x%5B1%5D=8, and y%5B1%5D=0



y-0=%28-2%2F3%29%2Ax%2B%282%2F3%29%288%29 Distribute -2%2F3



y-0=%28-2%2F3%29%2Ax%2B16%2F3 Multiply



y=%28-2%2F3%29%2Ax%2B16%2F3%2B0Add 0 to both sides to isolate y

y=%28-2%2F3%29%2Ax%2B16%2F3%2B0%2F3 Make into equivalent fractions with equal denominators



y=%28-2%2F3%29%2Ax%2B16%2F3 Combine the fractions



y=%28-2%2F3%29%2Ax%2B16%2F3 Reduce any fractions

So the equation of the line that is perpendicular to y=%283%2F2%29%2Ax-3 and goes through (8,0) is y=%28-2%2F3%29%2Ax%2B16%2F3


So here are the graphs of the equations y=%283%2F2%29%2Ax-3 and y=%28-2%2F3%29%2Ax%2B16%2F3




graph of the given equation y=%283%2F2%29%2Ax-3 (red) and graph of the line y=%28-2%2F3%29%2Ax%2B16%2F3(green) that is perpendicular to the given graph and goes through (8,0)

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation for the linear function g(x) which is perpendicular to the line 3x−2y=6 and intersects the line 3x−2y=6 at x=8.
g(x)=
***
Standard form of equation for a line: y=mx+b, m=slope, b=y-intercept
3x-2y=6
2y=3x-6
y=(3/2)x-3
slope=(3/2)
using given x-coordinate(x=8) of point of intersection to find y
y=(3/2)8-3=12-3=9
point of intersection:(8,9)
..
slope of line perpendicular to given line=-2/3 (negative reciprocal)
equation: y=(-2/3)x+b
solve for b using coordinates from point of intersection(8,9) on the line
b=9+2*8/3=9+16/3=43/3
equation:
g(x)=-2x/3+43/3