To find the slope of a line passing through two points, we can use the slope formula:

$\text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}$

For this line, the given points are:

• Point 1: $(-2, 5)$
• Point 2: $(2, -5)$

Step-by-Step Solution

1. Identify the coordinates:

   • $x_1 = -2$, $y_1 = 5$
   • $x_2 = 2$, $y_2 = -5$

2. Substitute these values into the formula: $m = \frac{-5 - 5}{2 - (-2)}$

3. Simplify the calculations:

   • The numerator: $-5 - 5 = -10$
   • The denominator: $2 - (-2) = 2 + 2 = 4$

   So, $m = \frac{-10}{4}$

4. Simplify the fraction: $m = \frac{-5}{2}$

Final Answer

The slope of the line is $-\frac{5}{2}$.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. What is the slope-intercept form of a line with a slope of $-\frac{5}{2}$ and a point $(2, -5)$ on it?
2. How do you determine if two lines are parallel by comparing their slopes?
3. What is the difference in slope between horizontal and vertical lines?
4. How would you calculate the y-intercept of this line?
5. Can you find the equation of the line passing through $(-2, 5)$ and $(2, -5)$?

Tip: The slope of a line indicates how steep the line is; a negative slope means the line goes downward from left to right.