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1. 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.

 

2. Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2), and is parallel to the graph of x + 3y = -5

 

3. Solve the inequality 2x - 5 < -x +12. Give your answer as an interval. 

(I thought this one was x < 17/3, but it's not)

 Sep 2, 2020
edited by VioIynx  Sep 2, 2020
 #1
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m + b = 3 + (-1) = 2.

 Sep 2, 2020
 #2
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2. From x + 3y = -5, y = -x/3 - 5, so the slope of the line is -1/3. The slope of the new line is also -1/3, so y = -x/3 + B.  Pugging in x = 2 and y = -7, we get -7 = -2/3 + B, so B = -19/3.

 

Then the line is y = -x/3 - 19/3.  Then 3y = -x - 19, so 3y + x = -19.  We want the right-hand side to be 3, so we mutiply both sides by -3/19: -9/19*y - 3/19*x = 3.  Therefore, B - A = -9/19 - 3/19 = -12/19.

 

3. The solution is (-5/3,inf).

 Sep 4, 2020

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