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Line $l_1$ represents the graph of $3x + 4y = -14$. Line $l_2$ passes through the point $(-5,7)$, and is perpendicular to line $l_1$. If line $l_2$ represents the graph of $y=mx +b$, then find $m+b$.

 Jun 29, 2020
 #1
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This is AoPS homework.  You should not cheat on your homework.

 Jun 29, 2020
 #2
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Most Guests here are "cheating" on their AoPS homework as well. How would we know if you aren't either, hm?

gwenspooner85  Jun 29, 2020
 #3
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We write 3x+4y=-14 in slope intercept form.

 

3x+4y=-14

4y=-3x-14

y=-3/4x-14/4

 

The slope of the perpendicular line must be 4/3 because the two slopes must multiply to -1. 

 

We plug in the slope into y=mx+b to get y=4/3x+b. Then we plug in the given point to determine b, the y-intercept.

 

7=4/3(-5)+b

7=-20/3+b

b=7+20/3

b=41/3

 

Therefore the equation of the perpendicular line is y=4/3x+41/3.

 Jun 29, 2020

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