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.
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