Point $A$ is at $(0, 0)$ and point $B$ is on the line $y = 4$. The slope of segment $AB$ is $\frac{2}{3}$. What is the sum of the $x$- and $y$-coordinates of point $B$?
I need to find the coordinates of point $B$, which is on the line $y = 4$ and has a slope of $\frac{2}{3}$ with point $A$. I can use the slope-intercept form of the equation of a line, which is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. In this case, $m = \frac{2}{3}$ and $b = 0$, since the line passes through the origin. So the equation of the line is $y = \frac{2}{3}x$. I also know that $y = 4$ for point $B$, so I can substitute that into the equation and solve for $x$. I get $4 = \frac{2}{3}x$, or $x = 6$. So the coordinates of point $B$ are $(6, 4)$. To find the sum of the $x$- and $y$-coordinates, I just add them up. I get $6 + 4 = 10$. 