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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!

Find the slope of a line parallel to the line whose equation is 5x - 2y = 2. Fully simplify your answer.

Learn how to find the slope of a line parallel to the equation 5x - 2y = 2. This problem explores the algebraic concept of parallel lines and requires converting the equation into slope-intercept form to identify the slope. Suitable for students in Grades 9-12.

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