SOLUTION: find the equation of the line that passes through the point (2,6) and is perpendicular to y= - 5/4x +1

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Question 336357: find the equation of the line that passes through the point (2,6) and is perpendicular to y= - 5/4x +1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We can see that the equation y=-%285%2F4%29x%2B1 has a slope m=-5%2F4 and a y-intercept b=1.


Now to find the slope of the perpendicular line, simply flip the slope m=-5%2F4 to get m=-4%2F5. Now change the sign to get m=4%2F5. So the perpendicular slope is m=4%2F5.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=4%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-6=%284%2F5%29%28x-2%29 Plug in m=4%2F5, x%5B1%5D=2, and y%5B1%5D=6


y-6=%284%2F5%29x%2B%284%2F5%29%28-2%29 Distribute


y-6=%284%2F5%29x-8%2F5 Multiply


y=%284%2F5%29x-8%2F5%2B6 Add 6 to both sides.


y=%284%2F5%29x%2B22%2F5 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to y=-%285%2F4%29x%2B1 that goes through the point is y=%284%2F5%29x%2B22%2F5.


Here's a graph to visually verify our answer:


Graph of the original equation y=-%285%2F4%29x%2B1 (red) and the perpendicular line y=%284%2F5%29x%2B22%2F5 (green) through the point .


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

Also, feel free to check out my website.

Jim