SOLUTION: Find the equation of the line perpendicular to 3x-4y=9 and passing through (2,-1). Write the equation in standard form, with all integer coefficients.

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line perpendicular to 3x-4y=9 and passing through (2,-1). Write the equation in standard form, with all integer coefficients.      Log On


   

Question 170177: Find the equation of the line perpendicular to 3x-4y=9 and passing through (2,-1). Write the equation in standard form, with all integer coefficients.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x-4y=9 Start with the given equation.


-4y=9-3x Subtract 3x from both sides.


-4y=-3x%2B9 Rearrange the terms.


y=%28-3x%2B9%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%28%28-3%29%2F%28-4%29%29x%2B%289%29%2F%28-4%29 Break up the fraction.


y=%283%2F4%29x-9%2F4 Reduce.


We can see that the equation y=%283%2F4%29x-9%2F4 has a slope m=3%2F4 and a y-intercept b=-9%2F4.


Now to find the slope of the perpendicular line, simply flip the slope m=3%2F4 to get m=4%2F3. Now change the sign to get m=-4%2F3. So the perpendicular slope is m=-4%2F3.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=3%2F4 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--1=%28-4%2F3%29%28x-2%29 Plug in m=-4%2F3, x%5B1%5D=2, and y%5B1%5D=-1


y%2B1=%28-4%2F3%29%28x-2%29 Rewrite y--1 as y%2B1


3%28y%2B1%29=-4%28x-2%29 Multiply both sides by 3 to clear the fraction


3y%2B3=-4x%2B8 Distribute


4x%2B3y=8-3 Subtract 3 from both sides. Add 4x to both sides.


4x%2B3y=5 Combine like terms.


So the equation of the line perpendicular to 3x-4y=9 that goes through the point in standard form is 4x%2B3y=5.