The problem requires finding the slope of the line passing through the points $(-1, -5)$ and $(1, 2)$, and then graphing the line.

Step 1: Calculate the Slope

The formula to calculate the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

For the points $(-1, -5)$ and $(1, 2)$:

$m = \frac{2 - (-5)}{1 - (-1)} = \frac{2 + 5}{1 + 1} = \frac{7}{2}$

So, the slope $m$ is $\frac{7}{2}$.

Step 2: Graph the Line

1. Plot the Points: Mark the points $(-1, -5)$ and $(1, 2)$ on the graph.
2. Draw the Line: Use a ruler to connect the two points to draw the line. The line should pass through both points and have the slope $\frac{7}{2}$.

Verification

The graph in the image confirms that the line has been correctly plotted with the slope $\frac{7}{2}$.

Would you like to explore this further or have any other questions? Here are some related questions you might find interesting:

1. How do you calculate the slope of a line when given two points?
2. What does the slope of a line represent in a real-world context?
3. How do you find the equation of a line given its slope and a point on the line?
4. Can the slope of a line be negative? If so, what does it indicate?
5. What are the different forms of linear equations?

Tip: When graphing a line, it helps to start by plotting the given points first and then draw the line using a straightedge to ensure accuracy.