The equation you provided is:

\[
2x + 5y = 10
\]

This is a linear equation in two variables, \(x\) and \(y\). It represents a straight line on the coordinate plane. We can solve for one variable in terms of the other to understand its relationship better.

### Solving for \(y\):
\[
5y = 10 - 2x
\]
\[
y = \frac{10 - 2x}{5}
\]
\[
y = 2 - \frac{2}{5}x
\]

So, the equation of the line in slope-intercept form is:
\[
y = -\frac{2}{5}x + 2
\]
Where:
- The slope of the line is \(-\frac{2}{5}\).
- The y-intercept is \(2\), meaning the line crosses the y-axis at \((0, 2)\).

### Graphical Interpretation:
This equation describes a line with a negative slope, meaning it decreases as \(x\) increases. The slope of \(-\frac{2}{5}\) indicates that for every 5 units increase in \(x\), \(y\) decreases by 2 units.

Would you like further details or to see a graph of this line?

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Here are 5 related questions to expand on this:
1. How do you calculate the x-intercept of a linear equation?
2. What does the slope of a line represent geometrically?
3. Can you rewrite the equation in terms of \(x\) instead of \(y\)?
4. How would this line change if the equation was \(2x + 5y = 15\)?
5. What are some methods to solve a system of linear equations?

**Tip:** When graphing, knowing both the slope and intercepts helps plot the line quickly and accurately.

Learn how to solve the linear equation 2x + 5y = 10 and express it in slope-intercept form. Discover key concepts like slope and y-intercept, and explore the graphical interpretation of this equation. Suitable for students in Grades 8-10.

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