SOLUTION: Find the equation for the line with y-intercept 3 that is perpendicular to the line: y=2/3x-4 Possible answers: A) 2y=6-3x; B) 2y=3x+6; C) 3y=9-2x; D) 3y=2x+9

Algebra ->  Graphs -> SOLUTION: Find the equation for the line with y-intercept 3 that is perpendicular to the line: y=2/3x-4 Possible answers: A) 2y=6-3x; B) 2y=3x+6; C) 3y=9-2x; D) 3y=2x+9      Log On


   

Question 113925: Find the equation for the line with y-intercept 3 that is perpendicular to the line: y=2/3x-4 Possible answers: A) 2y=6-3x; B) 2y=3x+6; C) 3y=9-2x; D) 3y=2x+9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember if a line has the y-intercept 3, then it goes through the point (0,3)

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 2%2F3, 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%282%2F3%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%283%2F2%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-3%2F2 Multiply the fractions.


So the perpendicular slope is -3%2F2



So now we know the slope of the unknown line is -3%2F2 (its the negative reciprocal of 2%2F3 from the line y=%282%2F3%29%2Ax-4). Also since the unknown line goes through (0,3), 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-3=%28-3%2F2%29%2A%28x-0%29 Plug in m=-3%2F2, x%5B1%5D=0, and y%5B1%5D=3



y-3=%28-3%2F2%29%2Ax%2B%283%2F2%29%280%29 Distribute -3%2F2



y-3=%28-3%2F2%29%2Ax-0%2F2 Multiply



y=%28-3%2F2%29%2Ax-0%2F2%2B3Add 3 to both sides to isolate y

y=%28-3%2F2%29%2Ax-0%2F2%2B6%2F2 Make into equivalent fractions with equal denominators



y=%28-3%2F2%29%2Ax%2B6%2F2 Combine the fractions



y=%28-3%2F2%29%2Ax%2B3 Reduce any fractions

So the equation of the line that is perpendicular to y=%282%2F3%29%2Ax-4 and goes through (0,3) is y=%28-3%2F2%29%2Ax%2B3


So here are the graphs of the equations y=%282%2F3%29%2Ax-4 and y=%28-3%2F2%29%2Ax%2B3




graph of the given equation y=%282%2F3%29%2Ax-4 (red) and graph of the line y=%28-3%2F2%29%2Ax%2B3(green) that is perpendicular to the given graph and goes through (0,3)





So if we multiply both sides of y=%28-3%2F2%29x%2B3 by 2 we get 2y=6-3x. So the answer is A)