SOLUTION: ok well we are doing this in geometry but its a review from algebra P(2,5); 4x-y=8 We have to write and equation of the line that passes through the point p and is perpendicular

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Question 252731: ok well we are doing this in geometry but its a review from algebra
P(2,5); 4x-y=8
We have to write and equation of the line that passes through the point p and is perpendicular to the line with the given equation
p(1,4); y=2x+4
P(5,3); y=5x+2
If you could please help because i am not following very well in my class
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



4x-y=8 Start with the given equation.


-y=8-4x Subtract 4x from both sides.


-y=-4x%2B8 Rearrange the terms.


y=%28-4x%2B8%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=%28%28-4%29%2F%28-1%29%29x%2B%288%29%2F%28-1%29 Break up the fraction.


y=4x-8 Reduce.


We can see that the equation y=4%2Ax-8 has a slope m=4 and a y-intercept b=-8.


Now to find the slope of the perpendicular line, simply flip the slope m=4 to get m=1%2F4. Now change the sign to get m=-1%2F4. So the perpendicular slope is m=-1%2F4.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-1%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=%28-1%2F4%29%28x-2%29 Plug in m=-1%2F4, x%5B1%5D=2, and y%5B1%5D=5


y-5=%28-1%2F4%29x%2B%28-1%2F4%29%28-2%29 Distribute


y-5=%28-1%2F4%29x%2B1%2F2 Multiply


y=%28-1%2F4%29x%2B1%2F2%2B5 Add 5 to both sides.


y=%28-1%2F4%29x%2B11%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 4x-y=8 that goes through the point is y=%28-1%2F4%29x%2B11%2F2.


Here's a graph to visually verify our answer:


Graph of the original equation y=4%2Ax-8 (red) and the perpendicular line y=%28-1%2F4%29x%2B11%2F2 (green) through the point .


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# 2



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


Now to find the slope of the perpendicular line, simply flip the slope m=2 to get m=1%2F2. Now change the sign to get m=-1%2F2. So the perpendicular slope is m=-1%2F2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-1%2F2 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=%28-1%2F2%29%28x-1%29 Plug in m=-1%2F2, x%5B1%5D=1, and y%5B1%5D=4


y-4=%28-1%2F2%29x%2B%28-1%2F2%29%28-1%29 Distribute


y-4=%28-1%2F2%29x%2B1%2F2 Multiply


y=%28-1%2F2%29x%2B1%2F2%2B4 Add 4 to both sides.


y=%28-1%2F2%29x%2B9%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to y=2x%2B4 that goes through the point is y=%28-1%2F2%29x%2B9%2F2.


Here's a graph to visually verify our answer:


Graph of the original equation y=2x%2B4 (red) and the perpendicular line y=%28-1%2F2%29x%2B9%2F2 (green) through the point .



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# 3




We can see that the equation y=5x%2B2 has a slope m=5 and a y-intercept b=2.


Now to find the slope of the perpendicular line, simply flip the slope m=5 to get m=1%2F5. Now change the sign to get m=-1%2F5. So the perpendicular slope is m=-1%2F5.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-1%2F5 and the coordinates of the given point .


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


y-3=%28-1%2F5%29%28x-5%29 Plug in m=-1%2F5, x%5B1%5D=5, and y%5B1%5D=3


y-3=%28-1%2F5%29x%2B%28-1%2F5%29%28-5%29 Distribute


y-3=%28-1%2F5%29x%2B1 Multiply


y=%28-1%2F5%29x%2B1%2B3 Add 3 to both sides.


y=%28-1%2F5%29x%2B4 Combine like terms.


So the equation of the line perpendicular to y=5x%2B2 that goes through the point is y=%28-1%2F5%29x%2B4.


Here's a graph to visually verify our answer:


Graph of the original equation y=5x%2B2 (red) and the perpendicular line y=%28-1%2F5%29x%2B4 (green) through the point .