Graph the line with slope \( -\frac{1}{2} \) passing through the point \( (-3,3) \)

To graph a line with a slope of \(-\frac{1}{2}\) passing through the point \((-3,3)\), it's essential to remember that the slope indicates how much the \(y\)-value changes for each unit change in the \(x\)-value. Starting from the point \((-3, 3)\), you can go one unit to the right (\(+1\) in \(x\)), and since the slope is negative, you'll move down half a unit in the \(y\)-direction. This gives you the next point \((-2, 2.5)\). Connecting these points and extending the line in both directions will give you the graph! You can also create a table of values to find additional points on the line. Just remember that for every two units you move to the right, you'll move down one unit—this will help you plot points more easily. The equation of the line is \(y - 3 = -\frac{1}{2}(x + 3)\), which you can rearrange into slope-intercept form, \(y = -\frac{1}{2}x + \frac{9}{2}\). Now you have a direct way to find \(y\) based on any \(x\) you choose!