To solve the problem, we need to find the slope of a line parallel to the line given by the equation:

$5x - 2y = 2$

Step 1: Convert the equation to slope-intercept form ( $y = mx + b$ ), where $m$ is the slope.

Starting with:

$5x - 2y = 2$

Isolate $y$:

$-2y = -5x + 2$

Now, divide by $-2$ to get:

$y = \frac{5}{2}x - 1$

Step 2: Identify the slope

In the slope-intercept form, $y = mx + b$, $m$ is the slope. Therefore, the slope of this line is:

$m = \frac{5}{2}$

Step 3: Slope of a parallel line

Since parallel lines have the same slope, the slope of any line parallel to the given line is also:

$m = \frac{5}{2}$

Thus, the slope of the parallel line is $\frac{5}{2}$.

Let me know if you'd like further clarification, or if you have any more questions.

Here are five related questions for further practice:

1. What is the slope of a line perpendicular to the line $5x - 2y = 2$?
2. How would you find the y-intercept of the line $5x - 2y = 2$?
3. What is the equation of a line parallel to $5x - 2y = 2$ and passing through the point $(0, 3)$?
4. Can you write the equation of a line perpendicular to $5x - 2y = 2$ and passing through $(1, 2)$?
5. How would you graph the line $y = \frac{5}{2}x - 1$?

Tip: Always remember that parallel lines have identical slopes, while perpendicular lines have slopes that are negative reciprocals of each other!