The given equation is:

$y = -\frac{1}{3}x - 2$

This is a linear equation in slope-intercept form:
$y = mx + b$ where:

• $m = -\frac{1}{3}$ is the slope of the line.
• $b = -2$ is the y-intercept (the point where the line crosses the y-axis).

Steps to Graph the Equation:

1. Plot the y-intercept ($b$):

   • When $x = 0$, $y = -2$.
     So, the line passes through the point $(0, -2)$.

2. Use the slope $m = -\frac{1}{3}$:

   • The slope means for every 1 unit increase in $x$, $y$ decreases by $\frac{1}{3}$.
   • Alternatively, move down 1 unit on the y-axis for every 3 units right on the x-axis.

3. Plot additional points using the slope:

   • From $(0, -2)$, move 3 units right to $x = 3$, and 1 unit down to $y = -3$.
     So, the point $(3, -3)$ lies on the line.
   • Similarly, you could move left 3 units and up 1 unit from $(0, -2)$, giving the point $(-3, -1)$.

4. Draw the line through the points:

   • Connect the points $(0, -2)$, $(3, -3)$, and $(-3, -1)$ with a straight line. The line will extend in both directions.

Would you like me to help draw the graph or confirm the line's behavior further?

Related Questions:

1. What does a negative slope indicate about a line?
2. How do you find the x-intercept of a line?
3. How would the graph change if the slope were positive?
4. What does changing the y-intercept do to the graph?
5. How do parallel lines relate to slope?

Tip: Remember, slope measures both the steepness and direction of the line!