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 \(m+b.\)
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 = 61/3
The question is asking for m + b
m = 4/3 and b = 61/3
m + b = 65/3
