Two lines defined by the equations $y = mx + 4$ and $y = 3x + b$, where $m$ and $b$ are constants, intersect at the point $(6, 10)$. What is the value of $b + m$?
I need to find the values of $b$ and $m$ that make the point $(6, 10)$ satisfy both equations. I can start by plugging in $x = 6$ and $y = 10$ into both equations and see what I get. For the first equation, I get $10 = m \cdot 6 + 4$, which simplifies to $m \cdot 6 = 6$, or $m = 1$. For the second equation, I get $10 = 3 \cdot 6 + b$, which simplifies to $b = -8$. Now I have both $b$ and $m$, so I can add them up to get the answer. $b + m = -8 + 1 = -7$. 