To graph the line with slope $-\frac{1}{3}$ passing through the point $(-1, 2)$, we can first derive the equation of the line using the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope of the line,
• $(x_1, y_1)$ is the point the line passes through.

Given:

• Slope $m = -\frac{1}{3}$,
• Point $(-1, 2)$.

Substituting into the point-slope form:

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

Now, we can simplify the equation:

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

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

$y = -\frac{1}{3}x + \frac{5}{3}$

This is the slope-intercept form of the line: $y = -\frac{1}{3}x + \frac{5}{3}$.

Now, to graph the line:

1. Plot the point $(-1, 2)$ on the coordinate plane.
2. Use the slope $-\frac{1}{3}$, which means for every 3 units you move to the right (positive $x$), move 1 unit down (negative $y$).
3. Draw the line passing through the plotted points.

Let me know if you would like further details or a step-by-step visual!

Here are some related questions to deepen your understanding:

1. How do you convert the point-slope form of a line to the slope-intercept form?
2. What are the characteristics of lines with negative slopes?
3. How does the slope affect the direction and steepness of a line?
4. How do you find the equation of a line given two points instead of a point and a slope?
5. How would you check if a point lies on a line given the line's equation?

Tip: When dealing with slopes, remember that a positive slope goes upwards to the right, while a negative slope goes downwards to the right.