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The correct answer is $\frac{18}{11}$. For a line that passes through the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ in the xy-plane, the slope of the line can be calculated using the slope formula, $m=\frac{y_2-y_1}{x_2-x_1}$. It's given that a line passes through the points $\left(4,6\right)$ and $\left(15,24\right)$ in the xy-plane. Substituting $\left(4,6\right)$ for $\left(x_1,y_1\right)$ and $\left(15,24\right)$ for $\left(x_2,y_2\right)$ in the slope formula, $m=\frac{y_2-y_1}{x_2-x_1}$, yields $m=\frac{24-6}{15-4}$, or $m=\frac{18}{11}$. Therefore, the slope of the line is $\frac{18}{11}$. Note that 18/11 and 1.636 are examples of ways to enter a correct answer.