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.