The equation $x + 3y = 10$ is a linear equation in two variables. Depending on the context, there are different ways to work with this equation. Let me provide an analysis:

1. Solving for $x$ or $y$

• Solve for $x$:
  $x = 10 - 3y$

• Solve for $y$:
  $y = \frac{10 - x}{3}$

2. Representing as a Graph

This equation can be rewritten in slope-intercept form: $y = -\frac{1}{3}x + \frac{10}{3}$

This represents a straight line with:

• Slope: $-\frac{1}{3}$
• Y-intercept: $\frac{10}{3}$

3. Example Solutions (points on the line)

You can find solutions by substituting values for $x$ or $y$:

• If $x = 4$: $y = \frac{10 - 4}{3} = 2$ → $(4, 2)$
• If $y = 0$: $x = 10$ → $(10, 0)$
• If $y = 1$: $x = 10 - 3(1) = 7$ → $(7, 1)$

4. Interpretation

The equation describes a relationship between $x$ and $y$ where every pair $(x, y)$ that satisfies it lies on a straight line in a 2D plane.

Would you like me to:

• Graph this equation?
• Explore specific solutions?
• Help with a related problem?

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Relative Questions:

1. How do we determine whether a specific point lies on this line?
2. What are the practical applications of linear equations in two variables?
3. How can this equation be represented in standard form and slope-intercept form?
4. How do we find the perpendicular or parallel line to this one?
5. What changes in the line if we modify the equation to $x + 3y = 15$?

Tip: To solve linear equations easily, always isolate one variable first and work systematically with substitutions!