The inequality $Y - X \geq 2$ can be rewritten or analyzed as follows:

Rearranged Form

$Y \geq X + 2$

This means that $Y$ must always be at least 2 units greater than $X$.

Graphical Representation

If plotted on a Cartesian plane:

1. Rewrite as $Y = X + 2$, which is the equation of a straight line.
2. The region above and including this line satisfies the inequality $Y - X \geq 2$.

The boundary line $Y = X + 2$ will be solid (indicating equality is included), and the area above the line represents the solution to the inequality.

Examples

For different $X$:

• If $X = 0$, then $Y \geq 2$.
• If $X = 3$, then $Y \geq 5$.
• If $X = -2$, then $Y \geq 0$.

Would you like a graph or further examples? Let me know!

Related Questions

1. How would this inequality change if it were $Y - X < 2$?
2. How do you represent $Y - X \geq 2$ in a real-world problem?
3. What does $Y - X \leq -2$ mean geometrically?
4. Can $Y - X \geq 2$ represent a system of inequalities with other constraints?
5. How does slope and y-intercept influence the solution region?

Tip

Always include the boundary line in your analysis unless explicitly excluded ($>$ or $<$ signs). This ensures accuracy when plotting or solving inequalities.