SAT Question e0f59119: Linear Equations In Two Variables answer and explanation with Desmos solution

A linear equation can be written in the form $y=mx+b$, where $m$ is the slope of the graph of the equation in the xy-plane and $\left(0,b\right)$ is the y-intercept. Distributing the $\frac{1}{3}$ in the equation $y=\frac{1}{3}\left(29x+10\right)+5x$ yields $y=\frac{29}{3}x+\frac{10}{3}+5x$. Combining like terms on the right-hand side of this equation yields $y=\frac{44}{3}x+\frac{10}{3}$. This equation is in the form $y=mx+b$, where $m=\frac{44}{3}$ and $b=\frac{10}{3}$. Therefore, the slope of the graph of the given equation in the xy-plane is $\frac{44}{3}$. Note that 44/3, 14.66, and 14.67 are examples of ways to enter a correct answer.