SOLUTION: Write an equation : through (0,9) perpendicular to 3x-2y=4

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Question 290409: Write an equation : through (0,9) perpendicular to 3x-2y=4
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
a point 0,9
and a line has to be perpendicular to 3x-2y=4
first write 3x-2y=4 in a form y=x%2Ba
3x-2y=4=
-2y=-3x%2B4........multiply by -1
2y=3x-4.........divide by 2
y=3x%2F2%2B4%2F2
y=%283%2F2%29x%2B2
y=%281.5%29x%2B2
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 1.5 (its from the slope of y=1.5%2Ax%2B2 which is also 1.5). Also since the unknown line goes through (0,9), 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-9=1.5%2A%28x-0%29 Plug in m=1.5, x%5B1%5D=0, and y%5B1%5D=9



y-9=1.5%2Ax-%281.5%29%280%29 Distribute 1.5



y-9=1.5%2Ax-0 Multiply



y=1.5%2Ax-0%2B9Add 9 to both sides to isolate y

y=1.5%2Ax%2B9 Combine like terms

So the equation of the line that is parallel to y=1.5%2Ax%2B2 and goes through (0,9) is y=1.5%2Ax%2B9


So here are the graphs of the equations y=1.5%2Ax%2B2 and y=1.5%2Ax%2B9



graph of the given equation y=1.5%2Ax%2B2 (red) and graph of the line y=1.5%2Ax%2B9(green) that is parallel to the given graph and goes through (0,9)