+20 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 $m+b$.
+781 Most Guests here are "cheating" on their AoPS homework as well. How would we know if you aren't either, hm?
+781 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.
