1. **Problem Statement:** Determine which lines pass through the point $(2,4)$ from the given lines: - Line A: $y=\frac{1}{2}x$ - Line B: $y=2x$ - Line C: $y=-x+6$ 2. **Method:** To check if a point lies on a line, substitute the $x$ and $y$ coordinates of the point into the line's equation. If the equation holds true, the point lies on that line. 3. **Check Line A:** Substitute $x=2$ into $y=\frac{1}{2}x$: $$y=\frac{1}{2}\times 2=1$$ Since $y=1 \neq 4$, the point $(2,4)$ is **not** on Line A. 4. **Check Line B:** Substitute $x=2$ into $y=2x$: $$y=2\times 2=4$$ Since $y=4$, the point $(2,4)$ **lies on Line B**. 5. **Check Line C:** Substitute $x=2$ into $y=-x+6$: $$y=-(2)+6=4$$ Since $y=4$, the point $(2,4)$ **lies on Line C**. 6. **Final Answer:** The lines that would be captured if the point $(2,4)$ were zapped are **Line B and Line C**. 7. **Explanation:** We selected lines by substituting the point's coordinates into each line's equation and checking if the equation is satisfied. Lines where the point satisfies the equation are the ones passing through that point.