SOLUTION: How do i do this? Write the equation of the line perpendicular to - 3x - 4y = 10 with a y-intercept of -5. Thank you.

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Question 200467: How do i do this? Write the equation of the line perpendicular to - 3x - 4y = 10 with a y-intercept of -5. Thank you.
Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
If a line has "a y-intercept of -5", then it goes through the point (0,-5)



-3x-4y=10 Start with the given equation.


-4y=10%2B3x Add 3x to both sides.


-4y=3x%2B10 Rearrange the terms.


y=%283x%2B10%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%28%283%29%2F%28-4%29%29x%2B%2810%29%2F%28-4%29 Break up the fraction.


y=-%283%2F4%29x-5%2F2 Reduce.


We can see that the equation y=-%283%2F4%29x-5%2F2 has a slope m=-3%2F4 and a y-intercept b=-5%2F2.


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--5=%284%2F3%29%28x-0%29 Plug in m=4%2F3, x%5B1%5D=0, and y%5B1%5D=-5


y%2B5=%284%2F3%29%28x-0%29 Rewrite y--5 as y%2B5


y%2B5=%284%2F3%29x-%284%2F3%29%280%29 Distribute


y%2B5=%284%2F3%29x%2B0 Multiply


y=%284%2F3%29x%2B0-5 Subtract 5 from both sides.


y=%284%2F3%29x-5 Combine like terms.


So the equation of the line perpendicular to -3x-4y=10 that goes through the point is y=%284%2F3%29x-5.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%283%2F4%29x-5%2F2 (red) and the perpendicular line y=%284%2F3%29x-5 (green) through the point .