The inequality provided is:

$y - x \geq 2$

Solution and Interpretation:

1. Rewriting the inequality: $y \geq x + 2$

2. Graphical Representation:

   • This represents a half-plane in a two-dimensional coordinate system.
   • The boundary line is $y = x + 2$, which is a straight line with a slope of $1$ and a $y$-intercept of $2$.
   • The inequality $y \geq x + 2$ means that the solution set includes all points on or above the line $y = x + 2$.

3. Graphing Steps:

   • Plot the line $y = x + 2$. It passes through the points:
     • $(0, 2)$ (when $x = 0$),
     • $(-2, 0)$ (when $y = 0$).
   • Since it is $\geq$, shade the region above the line.

Would you like me to plot this graph for you or explore specific cases? Let me know!

Follow-Up Questions:

1. What is the slope and intercept of the line $y = x + 2$, and how do they determine the line's properties?
2. How does the solution region of $y \geq x + 2$ differ from $y > x + 2$?
3. Can you identify two points that satisfy $y \geq x + 2$?
4. How would this inequality change if $y - x \leq 2$?
5. How would you graph $y = x + 2$ without using a calculator?

Tip:

Always start by plotting the equality boundary for inequalities and determine the correct region to shade by testing a point!