1. **State the problem:** We need to find the equation of the line in slope-intercept form $y=mx+b$ that represents the total number of appetizer recipes Zane knows ($y$) depending on the number of weeks he has attended culinary school ($x$). 2. **Identify given points:** The line passes through points $(0,0)$ and $(40,80)$. 3. **Calculate the slope $m$:** $$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{80 - 0}{40 - 0} = \frac{80}{40} = 2$$ 4. **Find the y-intercept $b$:** Since the line passes through $(0,0)$, the y-intercept is $b=0$. 5. **Write the equation:** Using $y=mx+b$, substitute $m=2$ and $b=0$: $$y=2x+0$$ 6. **Final answer:** $$\boxed{y=2x}$$ This means for each week Zane attends culinary school, he learns 2 new appetizer recipes.