To determine the slope of the given line, we use the slope formula:

$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1},$

where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Step 1: Identify two points on the line.

From the graph:

• Point 1: $(-4, -6)$,
• Point 2: $(2, 4)$.

Step 2: Apply the slope formula.

Substitute these points into the formula: $m = \frac{4 - (-6)}{2 - (-4)} = \frac{4 + 6}{2 + 4} = \frac{10}{6}.$

Step 3: Simplify the fraction.

$\frac{10}{6} = \frac{5}{3}.$

Final Answer:

The slope of the line is $\frac{5}{3}$.

Would you like more details on this solution or have any questions?

Here are five related questions to expand your understanding:

1. How does the slope indicate whether the line is increasing or decreasing?
2. What does a slope of $0$ represent geometrically?
3. Can you find the equation of the line using the slope and one point?
4. How would the slope change if the line was steeper?
5. What happens to the slope if the coordinates are switched (e.g., $(x_2, y_2)$ and $(x_1, y_1)$)?

Tip: Always double-check the coordinates chosen from the graph for accuracy to ensure correct calculations.