SOLUTION: Find the equation of the line with is perpendicular to the line y=−8x+9, and which passes through the point (−16, 6). y=(1/8)x+b (6)=(1/8)(-16) + b -3=b y=(1/8)

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line with is perpendicular to the line y=−8x+9, and which passes through the point (−16, 6). y=(1/8)x+b (6)=(1/8)(-16) + b -3=b y=(1/8)      Log On


   

Question 221407: Find the equation of the line with is perpendicular to the line y=−8x+9, and which passes through the point (−16, 6).
y=(1/8)x+b
(6)=(1/8)(-16) + b
-3=b
y=(1/8)x-3 <--- but this is wrong...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We can see that the equation y=-8x%2B9 has a slope m=-8 and a y-intercept b=9.


Now to find the slope of the perpendicular line, simply flip the slope m=-8 to get m=-1%2F8. Now change the sign to get m=1%2F8. So the perpendicular slope is m=1%2F8.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=1%2F8 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=%281%2F8%29%28x--16%29 Plug in m=1%2F8, x%5B1%5D=-16, and y%5B1%5D=6


y-6=%281%2F8%29%28x%2B16%29 Rewrite x--16 as x%2B16


y-6=%281%2F8%29x%2B%281%2F8%29%2816%29 Distribute


y-6=%281%2F8%29x%2B2 Multiply


y=%281%2F8%29x%2B2%2B6 Add 6 to both sides.


y=%281%2F8%29x%2B8 Combine like terms.


So the equation of the line perpendicular to y=-8x%2B9 that goes through the point is y=%281%2F8%29x%2B8.


Here's a graph to visually verify our answer:


Graph of the original equation y=-8x%2B9 (red) and the perpendicular line y=%281%2F8%29x%2B8 (green) through the point .

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