To find the slope of the line shown in the image, we use the formula for slope:

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

Step 1: Identify two points on the line

From the graph:

• One point is $(-4, 0)$ (on the x-axis).
• Another point is $(0, 2)$ (on the y-axis).

Step 2: Calculate the slope

Substitute the coordinates into the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}$

Final Answer:

The slope of the line is:

$m = \frac{1}{2}$

Would you like me to explain this further or solve a related problem? Here are five follow-up questions you might consider:

1. How do you interpret slope in the context of a graph?
2. What happens to the slope if the line is steeper?
3. How would you find the equation of the line passing through $(-4, 0)$ and $(0, 2)$?
4. Can a line have a slope of zero? What would it look like?
5. How does a negative slope differ from a positive slope?

Tip: The slope is a measure of how steep the line is; a larger slope means a steeper incline or decline!