To calculate the slope $m$ of the line shown in the image, we use the formula for slope:

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

We need to pick two points from the graph where the line passes through grid intersections. Observing the graph:

1. One point is $(-6, -4)$.
2. Another point is $(2, 2)$.

Now, substitute these coordinates into the slope formula:

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

Simplify the numerator and denominator:

$m = \frac{2 + 4}{2 + 6} = \frac{6}{8}$

Reduce the fraction to its simplest form:

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

Thus, the slope of the line is:

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

Let me know if you'd like further explanation or need help with another step!

Questions for further practice:

1. How would you find the slope if the line passed through $(3, 5)$ and $(7, 9)$?
2. What does a slope of 0 mean about a line's direction?
3. How would the slope change if the line was reflected across the x-axis?
4. How do you interpret the slope of a vertical line in mathematical terms?
5. What is the equation of a line with slope $\frac{3}{4}$ passing through $(2, 2)$?

Tip: Always check that the points chosen lie exactly on the grid intersections to avoid errors in slope calculations.