SOLUTION: I have been trying for hours to solve the following type of equations and get stuck toward the end. Any help you can provide would be greatly appreciated. The following is the pro

Algebra ->  Linear-equations -> SOLUTION: I have been trying for hours to solve the following type of equations and get stuck toward the end. Any help you can provide would be greatly appreciated. The following is the pro      Log On


   

Question 376122: I have been trying for hours to solve the following type of equations and get stuck toward the end. Any help you can provide would be greatly appreciated. The following is the problem and below is what I am trying:
Write an equation of the line containing the given point and perpendicular to the given line
(9, -4); 6x + 5y = 4
ME: 5y=-6x+4
y= 6/5x+4/5
y-(-4)=6/5(x-9)
I believe I have to subtract 4 from each side but this is where I keep getting confused. Thanks in advance for any help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%2B5y=4 Start with the given equation.


5y=4-6x Subtract 6x from both sides.


5y=-6x%2B4 Rearrange the terms.


y=%28-6x%2B4%29%2F%285%29 Divide both sides by 5 to isolate y.


y=%28%28-6%29%2F%285%29%29x%2B%284%29%2F%285%29 Break up the fraction.


y=-%286%2F5%29x%2B4%2F5 Reduce.


We can see that the equation y=-%286%2F5%29x%2B4%2F5 has a slope m=-6%2F5 and a y-intercept b=4%2F5.


Now to find the slope of the perpendicular line, simply flip the slope m=-6%2F5 to get m=-5%2F6. Now change the sign to get m=5%2F6. So the perpendicular slope is m=5%2F6.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=5%2F6 and the coordinates of the given point .


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


y--4=%285%2F6%29%28x-9%29 Plug in m=5%2F6, x%5B1%5D=9, and y%5B1%5D=-4


y%2B4=%285%2F6%29%28x-9%29 Rewrite y--4 as y%2B4. Recall that subtracting a negative is the same as adding a positive.


y%2B4=%285%2F6%29x%2B%285%2F6%29%28-9%29 Distribute


y%2B4=%285%2F6%29x-15%2F2 Multiply


y=%285%2F6%29x-15%2F2-4 Subtract 4 from both sides.


y=%285%2F6%29x-23%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 6x%2B5y=4 that goes through the point is y=%285%2F6%29x-23%2F2.


Here's a graph to visually verify our answer:


Graph of the original equation y=-%286%2F5%29x%2B4%2F5 (red) and the perpendicular line y=%285%2F6%29x-23%2F2 (green) through the point .


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim