SOLUTION: Give the slope-intercept form of the equation of the line that is perpendicular to 5x + 4y + 4 and contains (-1, 9).

Algebra ->  Linear-equations -> SOLUTION: Give the slope-intercept form of the equation of the line that is perpendicular to 5x + 4y + 4 and contains (-1, 9).      Log On


   

Question 173085: Give the slope-intercept form of the equation of the line that is perpendicular to 5x + 4y + 4 and contains (-1, 9).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the equation supposed to be 5x+%2B+4y+=+4. I'll assume that it is.




5x%2B4y=4 Start with the given equation.


4y=4-5x Subtract 5x from both sides.


4y=-5x%2B4 Rearrange the terms.


y=%28-5x%2B4%29%2F%284%29 Divide both sides by 4 to isolate y.


y=%28%28-5%29%2F%284%29%29x%2B%284%29%2F%284%29 Break up the fraction.


y=-%285%2F4%29x%2B1 Reduce.


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=-5%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-9=%284%2F5%29%28x--1%29 Plug in m=4%2F5, x%5B1%5D=-1, and y%5B1%5D=9


y-9=%284%2F5%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-9=%284%2F5%29x%2B%284%2F5%29%281%29 Distribute


y-9=%284%2F5%29x%2B4%2F5 Multiply


y=%284%2F5%29x%2B4%2F5%2B9 Add 9 to both sides.


y=%284%2F5%29x%2B49%2F5 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 5x%2B4y=4 that goes through the point is y=%284%2F5%29x%2B49%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%2B49%2F5 (green) through the point .