1. **State the problem:** We are given two points from a fundraiser: at week 3, $600 was raised, and at week 5, $1000 was raised. We want to find a linear function relating weeks ($x$) to money raised ($y$), and identify two additional points on this line. 2. **Formula and rules:** A linear function has the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** Using points $(3,600)$ and $(5,1000)$, $$m = \frac{1000 - 600}{5 - 3} = \frac{400}{2} = 200$$ 4. **Find the y-intercept $b$:** Use point $(3,600)$, $$600 = 200 \times 3 + b \implies b = 600 - 600 = 0$$ 5. **Write the linear function:** $$y = 200x + 0 = 200x$$ 6. **Find two additional points:** Choose $x=1$ and $x=7$, - For $x=1$: $$y = 200 \times 1 = 200$$ - For $x=7$: $$y = 200 \times 7 = 1400$$ So two additional points are $(1, 200)$ and $(7, 1400)$. 7. **Explanation:** The function $y=200x$ means the school raises 200 units of money each week. The points $(3,600)$ and $(5,1000)$ fit this line, and so do the additional points we found. **Final answer:** The linear function is $$y=200x$$ and two additional points are $(1, 200)$ and $(7, 1400)$.