The inequality $y_1 - y_2 \geq 0$ translates to determining the regions where the graph of $y_1$ is greater than or equal to the graph of $y_2$. The graph shows two lines, $y_1$ (blue line) and $y_2$ (red line), crossing at the point $(2, 1)$.

To solve this inequality, we need to find where $y_1 \geq y_2$. This happens when the blue line is above the red line or they are equal.

Solution Process:

1. Intersection Point: At the point $(2, 1)$, the two lines intersect, meaning $y_1 = y_2$ at $x = 2$.
2. Left of the Intersection: For $x \leq 2$, the blue line ( $y_1$ ) is above the red line ( $y_2$ ), meaning $y_1 > y_2$.
3. Right of the Intersection: For $x > 2$, the red line ( $y_2$ ) is above the blue line ( $y_1$ ), meaning $y_1 < y_2$.

Conclusion:

The solution for $y_1 - y_2 \geq 0$ is for $x \leq 2$, and the inequality holds at $x = 2$ as well because of the "greater than or equal to" condition.

Solution in interval notation:

$(-\infty, 2]$

Would you like further clarification or details?

Here are some related questions:

1. What is the significance of the intersection point between two functions?
2. How do you interpret inequality conditions like $y_1 - y_2 \geq 0$ geometrically?
3. Can we apply this process to non-linear functions?
4. What changes if the inequality was $y_1 - y_2 > 0$ instead?
5. How would this solution change if $y_1$ and $y_2$ had different slopes?

Tip: Always pay attention to whether the inequality includes the "equal to" condition, as it changes whether the boundary point is included in the solution set.