SOLUTION: Find an equation of the line satisfying the given conditions. Write the equation in slope-intercept form. Through(-5,-2);perpendicular to -5x-2y=27

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line satisfying the given conditions. Write the equation in slope-intercept form. Through(-5,-2);perpendicular to -5x-2y=27      Log On


   

Question 171552: Find an equation of the line satisfying the given conditions. Write the equation in slope-intercept form.
Through(-5,-2);perpendicular to -5x-2y=27
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-5x-2y=27 Start with the given equation.


-2y=27%2B5x Add 5x to both sides.


-2y=5x%2B27 Rearrange the terms.


y=%285x%2B27%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=%28%285%29%2F%28-2%29%29x%2B%2827%29%2F%28-2%29 Break up the fraction.


y=-%285%2F2%29x-27%2F2 Reduce.


We can see that the equation y=-%285%2F2%29x-27%2F2 has a slope m=-5%2F2 and a y-intercept b=-27%2F2.


Now to find the slope of the perpendicular line, simply flip the slope m=-5%2F2 to get m=-2%2F5. Now change the sign to get m=2%2F5. So the perpendicular slope is m=2%2F5.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-5%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--2=%282%2F5%29%28x--5%29 Plug in m=2%2F5, x%5B1%5D=-5, and y%5B1%5D=-2


y--2=%282%2F5%29%28x%2B5%29 Rewrite x--5 as x%2B5


y%2B2=%282%2F5%29%28x%2B5%29 Rewrite y--2 as y%2B2


y%2B2=%282%2F5%29x%2B%282%2F5%29%285%29 Distribute


y%2B2=%282%2F5%29x%2B2 Multiply


y=%282%2F5%29x%2B2-2 Subtract 2 from both sides.


y=%282%2F5%29x%2B0 Combine like terms.


y=%282%2F5%29x Remove the trailing zero


So the equation of the line perpendicular to -5x-2y=27 that goes through the point is y=%282%2F5%29x.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%285%2F2%29x-27%2F2 (red) and the perpendicular line y=%282%2F5%29x (green) through the point .