To find the slope of the line graphed in the image, we can use the formula for the slope between two points:

$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

From the graph, we can identify two points where the line crosses grid intersections clearly:

1. The first point is approximately $(-4, 4)$.
2. The second point is $(4, -2)$.

Now, applying these values into the slope formula:

$m = \frac{{-2 - 4}}{{4 - (-4)}} = \frac{{-6}}{{4 + 4}} = \frac{{-6}}{{8}} = -\frac{3}{4}$

Thus, the slope of the line is:

$m = -\frac{3}{4}$

Would you like any additional details or have further questions?

Here are 5 related questions you might find useful:

1. How does the slope of a line relate to its steepness?
2. What happens to the slope if the line becomes vertical or horizontal?
3. How do you find the equation of a line given its slope and a point?
4. What is the significance of a positive versus negative slope?
5. How would the graph change if the slope were $-1$ instead of $-\frac{3}{4}$?

Tip: Always remember that a negative slope means the line is decreasing from left to right, and a positive slope means it's increasing.