1. **Problem Statement:** Label each graph with the correct equation from the given list: - $y = 2x$ - $y = -\frac{1}{2}x - 1$ - $y = 3x + 2$ - $y = -\frac{1}{2}x + 1$ 2. **Understanding the problem:** Each graph is a straight line represented by the equation $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 3. **Step-by-step labeling:** - The first graph (top-left) passes through the origin $(0,0)$ and has a positive slope. Since it passes through $(0,0)$, $c=0$. Among the options, $y=2x$ fits because slope $m=2$ and $c=0$. - The second graph (top-right, second from left) has a negative slope and crosses the y-axis at $-1$. This matches $y = -\frac{1}{2}x - 1$ where $m = -\frac{1}{2}$ and $c = -1$. - The third graph (top-right, second from right) has a positive slope and crosses the y-axis at $2$. This matches $y = 3x + 2$ where $m=3$ and $c=2$. - The fourth graph (top-right, rightmost) has a negative slope and crosses the y-axis at $1$. This matches $y = -\frac{1}{2}x + 1$ where $m = -\frac{1}{2}$ and $c=1$. 4. **Final answer:** - First graph: $y = 2x$ - Second graph: $y = -\frac{1}{2}x - 1$ - Third graph: $y = 3x + 2$ - Fourth graph: $y = -\frac{1}{2}x + 1$