Questions on Algebra: Linear Equations, Graphs, Slope answered by real tutors!

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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.: 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(9921) 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+9 Rearrange the terms.


y=(-3x+9)/(-4) Divide both sides by -4 to isolate y.


y=((-3)/(-4))x+(9)/(-4) Break up the fraction.


y=(3/4)x-9/4 Reduce.


We can see that the equation y=(3/4)x-9/4 has a slope m=3/4 and a y-intercept b=-9/4.


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


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=3/4 and the coordinates of the given point .


y-y[1]=m(x-x[1]) Start with the point slope formula


y--1=(-4/3)(x-2) Plug in m=-4/3, x[1]=2, and y[1]=-1


y+1=(-4/3)(x-2) Rewrite y--1 as y+1


3(y+1)=-4(x-2) Multiply both sides by 3 to clear the fraction


3y+3=-4x+8 Distribute


4x+3y=8-3 Subtract 3 from both sides. Add 4x to both sides.


4x+3y=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+3y=5.