Let's analyze the function given in the image:

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

Step 1: Identify the Slope and Y-intercept

In the slope-intercept form $y = mx + b$, the values represent:

• $m$ (the slope) = $-\frac{1}{3}$
• $b$ (the y-intercept) = $-2$

So:

• Slope: $-\frac{1}{3}$
• Y-intercept: $-2$

Step 2: Graphing the Line

1. Plot the Y-intercept: Start by plotting the point $(0, -2)$ on the y-axis.
2. Use the Slope: The slope of $-\frac{1}{3}$ means that for each step to the right by 3 units, the line will go down by 1 unit. From $(0, -2)$:
   • Move 3 units to the right and 1 unit down to reach the point $(3, -3)$.
3. Draw the Line: Connect these two points to extend the line across the grid.

Would you like further assistance with the steps for graphing?

Related Questions:

1. What does a negative slope indicate about the direction of the line?
2. How would the graph change if the y-intercept were positive?
3. What would happen to the graph if the slope were $\frac{1}{3}$ instead?
4. How can you find the x-intercept of this line?
5. How do you interpret a fraction as a slope on a graph?

Tip:

When plotting a line, the y-intercept is a helpful starting point, and the slope guides how you move across the grid from that point.