Line Intersection 46144E
1. **State the problem:** We are given five linear equations and asked to find specific points or coordinates related to each line, such as where the line intersects $y=5$, the $x$-coordinate when $y=1$, the point where the line intersects $y=0$, the $x$-coordinate when $y=-1$, and the $y$-intercept.
2. **Recall the slope-intercept form:** Each line is given as $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.
3. **Find the points for the first line $y=2x+1$:**
- Intersect $y=5$: Set $5=2x+1 \Rightarrow 2x=4 \Rightarrow x=2$. Point is $(2,5)$.
- $x$ when $y=1$: Set $1=2x+1 \Rightarrow 2x=0 \Rightarrow x=0$.
- Intersect $y=0$: Set $0=2x+1 \Rightarrow 2x=-1 \Rightarrow x=-\frac{1}{2}$, point $(-\frac{1}{2},0)$.
- $x$ when $y=-1$: Set $-1=2x+1 \Rightarrow 2x=-2 \Rightarrow x=-1$.
- $y$-intercept is $b=1$, point $(0,1)$.
4. **Summary for first line:**
- Intersect $y=5$: $(2,5)$
- $x$ at $y=1$: $0$
- Intersect $y=0$: $(-\frac{1}{2},0)$
- $x$ at $y=-1$: $-1$
- $y$-intercept: $(0,1)$
5. **Check suspect list for matches:**
- Suspect F is $(2,5)$ which matches the intersect at $y=5$ for the first line.
**Final answer:** The point where the line $y=2x+1$ intersects $y=5$ is $(2,5)$, which corresponds to Suspect F.