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

 Feb 29, 2020
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Line 1 has the equation of 3x+4y = -14. I'm going to change this into slope intercept form

 

4y = -14 - 3x

y = -3x/4 - 7/2 This shows that the slope is -3/4. A  function perpendicular to this would have a slope of 4/3. For 2 linear functions to be perpendicular their slopes must be negative reciprocals. 

 

So line 2 so far has the equation y = 4x/3 + b

The question gives that this function passes through point -5,7, and we can plug this into the equation

 

7 = 4(-5)/3 + b

7 = -20/3 + b

b = 7 + 20/3

b = 21/3 + 20/3

b = 41/3

The question is asking for m + b

m = 4/3 and b = 41/3

m + b = 4/3 + 41/3 = 45/3

 

 

m + b = 15

 Feb 29, 2020

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