1. The problem asks to find the equation of the line in the form $y=mx$ that models the relationship between the number of weeks ($x$) and the number of books ($y$) based on the given points. 2. The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Using the points $(4, 10)$ and $(8, 30)$: $$m = \frac{30 - 10}{8 - 4} = \frac{20}{4}$$ 4. Simplify the fraction: $$m = \frac{\cancel{20}}{\cancel{4}} = 5$$ 5. Check with another pair of points $(8, 30)$ and $(12, 50)$: $$m = \frac{50 - 30}{12 - 8} = \frac{20}{4} = 5$$ 6. Since the slope $m$ is consistent, the equation of the line is: $$y = 5x$$ 7. None of the provided options exactly match $y=5x$, so the closest correct slope based on the data is $m=5$. Final answer: $y=5x$