Question

graph the line with slope $-\frac{1}{3}$ passing through the point $(-1, -2)$.\
graph grid and drawing tools omitted

Explanation:

Step1: Plot the given point

Locate the point \((-1, -2)\) on the coordinate plane. The \(x\)-coordinate is \(-1\) and the \(y\)-coordinate is \(-2\), so find the intersection of \(x = -1\) and \(y = -2\) and mark it.

Step2: Use the slope to find another point

The slope \(m = -\frac{1}{3}\) means for a change in \(x\) (run) of \(3\) units (positive or negative), the change in \(y\) (rise) is \(-1\) unit (since slope is \(\frac{\text{rise}}{\text{run}}\)). Starting from \((-1, -2)\), if we move \(3\) units to the right (increase \(x\) by \(3\), so \(x = -1 + 3 = 2\)) and \(1\) unit down (decrease \(y\) by \(1\), so \(y = -2 - 1 = -3\)), we get the point \((2, -3)\). Alternatively, we can move \(3\) units to the left ( \(x = -1 - 3 = -4\)) and \(1\) unit up ( \(y = -2 + 1 = -1\)) to get \((-4, -1)\).

Step3: Draw the line

Once we have two points (e.g., \((-1, -2)\) and \((2, -3)\) or \((-1, -2)\) and \((-4, -1)\)), draw a straight line passing through these points. This line will have a slope of \(-\frac{1}{3}\) and pass through \((-1, -2)\).

(Note: Since the problem is about graphing, the final answer is the graph of the line with the described slope and passing through the given point. The steps above guide how to construct that graph.)

Answer:

The graph is a straight line passing through \((-1, -2)\) with a slope of \(-\frac{1}{3}\) (constructed by plotting the point and using the slope to find another point to draw the line).