The given equation is:

$x + 2y - 1 = 0$

To analyze and work with this equation, you can:

Solve for $x$:

Rearrange the equation to isolate $x$: $x = 1 - 2y$

Solve for $y$:

Rearrange the equation to isolate $y$: $2y = 1 - x \quad \Rightarrow \quad y = \frac{1 - x}{2}$

Interpretation:

This is a linear equation representing a straight line in a two-dimensional coordinate system. The slope-intercept form of the line is: $y = -\frac{1}{2}x + \frac{1}{2}$ where:

• Slope ($m$) = $-\frac{1}{2}$
• Y-intercept ($b$) = $\frac{1}{2}$

Would you like a graphical representation or further elaboration?

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Here are 5 related questions you might explore:

1. What is the slope of the line represented by this equation?
2. How do you find the x-intercept of this line?
3. Can you determine if two given points lie on this line?
4. How would you write the equation if it passed through a specific point and had a given slope?
5. How does this line interact with another line (e.g., finding intersection points)?

Tip:

When analyzing a line, always rewrite the equation in slope-intercept form to easily understand its properties!