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Let line $l_1$ be the graph of $5x + 8y = -9$. Line $l_2$ is perpendicular to line $l_1$ and passes through the point $(10,10)$. If line $l_2$ is the graph of the equation $y=mx +b$, then find $m+b$.

 Jan 7, 2020
 #1
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5x + 8y = -9      subtract   5x  from both sides

 

8y  =   -5x   - 9                divide both sides  by  8

 

y = (-5/8)x - (9/8)

 

The slope of this line   is   -5/8

 

So.....the  slope of a perpendicular line is     8/5

 

Since this line passes  through   (10,10)  we have that

 

y = (8/5) (x - 10) +10     simplify

 

y = (8/5)x  - 80/5 + 50/5

 

y= (8/5) x  -  30/5

 

m = 8/5      b = -30/5

 

So

 

m +  b =    -22/ 5

 

 

cool cool cool

 Jan 7, 2020

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