Graph the line. \[ 3 x+y=-3 \]

To graph the line given by the equation \(3x + y = -3\), first rewrite it in slope-intercept form \(y = mx + b\). Rearranging gives \(y = -3x - 3\). This tells us that the slope \(m\) is -3, which means the line descends as it moves to the right. The y-intercept \(b\) is -3, meaning the line crosses the y-axis at the point (0, -3). You can plot this point and then use the slope to find another point. From (0, -3), move down 3 units and right 1 unit to reach the point (1, -6). Connecting these points will yield the line! To verify your line, find the intercepts. For the x-intercept, set \(y = 0\): \(3x = -3\) giving \(x = -1\). So, the x-intercept is (-1, 0). You’ll now have two key points: (0, -3) and (-1, 0). The line will thus cut through both of these, and you can draw your graph confidently knowing it’s correct!