1. The problem is to match each system of linear equations to its corresponding graph based on slopes and y-intercepts. 2. Recall that the slope-intercept form of a line is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. 3. Analyze each graph's lines: - Graph 1: Red line slope < 3, y-intercept ~1; Blue line slope 3, y-intercept 2. - Graph 2: Red line slope 3, y-intercept 3; Blue line slope 1, y-intercept 2. - Graph 3: Red line slope 2, y-intercept 3; Blue line slope 1, y-intercept 5. - Graph 4: Red line slope 2, y-intercept -2; Blue line slope 1, y-intercept -2. 4. Match each system: - System with $y=2x+1$ and $y=3x+2$ matches Graph 1 (red slope 2, intercept 1; blue slope 3, intercept 2). - System with $y=3x$ and $y=x+3$ matches Graph 2 (red slope 3, intercept 0; blue slope 1, intercept 3). But graph 2 blue intercept is 2, so check carefully. - System with $y=2x+3$ and $y=x+5$ matches Graph 3 (red slope 2, intercept 3; blue slope 1, intercept 5). - System with $y=2x-2$ and $y=x-2$ matches Graph 4 (red slope 2, intercept -2; blue slope 1, intercept -2). 5. Correcting Graph 2: red line slope 3, intercept 3; blue line slope 1, intercept 2. So system is $y=3x+3$ and $y=x+2$. 6. Final matches: - Graph 1: $y=2x+1$, $y=3x+2$ - Graph 2: $y=3x+3$, $y=x+2$ - Graph 3: $y=2x+3$, $y=x+5$ - Graph 4: $y=2x-2$, $y=x-2$