To find the slope of the line shown in the graph, we need to use the formula for slope:

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

By looking at the graph, we can choose two points on the line to calculate the slope. Let’s take two clear points:

• Point 1: $(-4, -1)$
• Point 2: $(0, -3)$

Now, applying the slope formula:

$\text{slope} = \frac{{-3 - (-1)}}{{0 - (-4)}} = \frac{{-3 + 1}}{{4}} = \frac{{-2}}{{4}} = -\frac{1}{2}$

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

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:

1. What is the y-intercept of the line shown?
2. How do you calculate the slope if given two arbitrary points?
3. Can the slope of a line be positive or zero? What does that mean geometrically?
4. How would the graph change if the slope were doubled?
5. Can we derive the equation of the line from this graph?

Tip: The slope represents the rate of change of $y$ with respect to $x$. Negative slope means the line decreases as $x$ increases.