SOLUTION: Find an equation in the form y=mx+b(where possible) for eacjh line. Through (0,5), perpendicular to 8x+5y=3

Algebra ->  Linear-equations -> SOLUTION: Find an equation in the form y=mx+b(where possible) for eacjh line. Through (0,5), perpendicular to 8x+5y=3      Log On


   

Question 145614This question is from textbook Finite Mathematics
: Find an equation in the form y=mx+b(where possible) for eacjh line.
Through (0,5), perpendicular to 8x+5y=3 This question is from textbook Finite Mathematics

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x%2B5y=3 Start with the given equation.


y=-%288%2F5%29x%2B3%2F5 Solve for y.


We can see that the equation y=-%288%2F5%29x%2B3%2F5 has a slope m=-8%2F5 and a y-intercept b=3%2F5.


Now to find the slope of the perpendicular line, simply flip the slope m=-8%2F5 to get m=-5%2F8. Now change the sign to get m=5%2F8. So the perpendicular slope is m=5%2F8.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-8%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-5=%285%2F8%29%28x-0%29 Plug in m=5%2F8, x%5B1%5D=0, and y%5B1%5D=5


y-5=%285%2F8%29x%2B%285%2F8%29%28-0%29 Distribute


y-5=%285%2F8%29x%2B0 Multiply


y=%285%2F8%29x%2B0%2B5 Add 5 to both sides.


y=%285%2F8%29x%2B5 Combine like terms.


So the equation of the line perpendicular to 8x%2B5y=3 that goes through the point is y=%285%2F8%29x%2B5.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%288%2F5%29x%2B3%2F5 (red) and the perpendicular line y=%285%2F8%29x%2B5 (green) through the point .