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To find the slope of the line represented by the equation \( 2x - 5y = 9 \), we can rewrite the equation in slope-intercept form, which is \( y = mx + b \), where \( m \) represents the slope.

### Steps:
1. Start with the given equation:
   \[
   2x - 5y = 9
   \]
   
2. Solve for \( y \):
   \[
   -5y = -2x + 9 \quad (\text{Subtract } 2x \text{ from both sides})
   \]
   \[
   y = \frac{-2x + 9}{-5} \quad (\text{Divide by } -5 \text{ on both sides})
   \]
   
3. Simplify the equation:
   \[
   y = \frac{2}{5}x - \frac{9}{5}
   \]
   
Now the equation is in slope-intercept form: \( y = \frac{2}{5}x - \frac{9}{5} \). The slope \( m \) is the coefficient of \( x \), which is \( \frac{2}{5} \).

### Answer:
The slope of the line is \( \frac{2}{5} \), so the correct choice is **D**.

Would you like further details, or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you find the slope of a line if the equation is given in standard form?
2. Can you convert a slope-intercept form equation back to standard form?
3. What is the geometric meaning of the slope in terms of rise over run?
4. How would you find the slope if the line passes through two given points?
5. What is the significance of the y-intercept in the slope-intercept form?

**Tip:** When solving for slope, isolating \( y \) in terms of \( x \) is key, as it reveals both the slope and y-intercept directly.

What is the slope of the line represented by the equation 2x - 5y = 9?

Learn how to find the slope of the line represented by the equation 2x - 5y = 9 by converting it to slope-intercept form. This step-by-step guide includes key algebraic concepts and formulas, suitable for students in Grades 7-10.

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