To find the slope of the line shown in the graph, we can use the formula for the slope between two points on the line, which is:

$\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

Steps:

1. Identify two points on the line. From the graph:

   • One point is $(2, 1)$.
   • Another point is $(-4, 4)$.

2. Use the slope formula: $\text{slope} = \frac{1 - 4}{2 - (-4)} = \frac{-3}{2 + 4} = \frac{-3}{6} = -\frac{1}{2}$

Conclusion:

The slope of the line is $-\frac{1}{2}$.

Would you like a more detailed explanation or have any questions?

Related questions:

1. How do you interpret a negative slope in a graph?
2. What does the slope tell us about the steepness of a line?
3. Can the slope of a horizontal line ever be negative?
4. How does the slope relate to the equation of a line in slope-intercept form?
5. What is the significance of the y-intercept in relation to the slope?

Tip:

To quickly determine the slope from a graph, look for two clear points on the line and count the "rise" over "run."