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The problem asks to find the slope of the line represented by the equation:

\[
5x - 2y = 20
\]

To determine the slope of a linear equation, we need to express it in slope-intercept form, which is:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

### Steps:
1. Start with the given equation:
   \[
   5x - 2y = 20
   \]
   
2. Solve for \(y\):
   - Subtract \(5x\) from both sides:
     \[
     -2y = -5x + 20
     \]
   - Divide through by \(-2\) to isolate \(y\):
     \[
     y = \frac{5}{2}x - 10
     \]

Now, we can see that the slope \(m\) is \(\frac{5}{2}\).

So, the correct answer is **c. \( \frac{5}{2} \)**.

Would you like more details on this process or have any questions?

Here are 5 related questions to explore further:
1. How can you determine the y-intercept from the equation \(5x - 2y = 20\)?
2. What is the slope of a line perpendicular to \(5x - 2y = 20\)?
3. How would you find the x-intercept of the same line?
4. How do you convert a line equation from point-slope form to slope-intercept form?
5. What does the slope represent in a real-world context?

**Tip:** Remember, a positive slope means the line goes upwards from left to right, while a negative slope means it goes downwards!

What is the slope of the graph of 5x - 2y = 20?

Learn how to find the slope of the linear equation 5x - 2y = 20. This problem involves algebraic manipulation to convert the equation to slope-intercept form (y = mx + b) and solve for the slope, m. Suitable for students in Grades 8-10.

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