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)=

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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)   (Show Source): You can put this solution on YOUR website!
given:

the linear function g(x) which is perpendicular to and
intersection point at : (,)
...first solve for



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 , you can find the perpendicular slope by this formula:

where is the perpendicular slope


So plug in the given slope to find the perpendicular slope



When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second



Multiply the fractions.


So the perpendicular slope is



So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). 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:

where m is the slope and (,) is the given point



Plug in , , and



Distribute



Multiply



Add to both sides to isolate y

Make into equivalent fractions with equal denominators



Combine the fractions



Reduce any fractions

So the equation of the line that is perpendicular to and goes through (,) is


So here are the graphs of the equations and




graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)
Answer by lwsshak3(11628)   (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

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