Subjects algebra

Line Intersection 46144E

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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.