To determine if the point $(1, 4)$ satisfies the inequality $y \geq 3x + 1$, we need to substitute $x = 1$ and $y = 4$ into the inequality and check if the inequality holds.

The inequality is: $y \geq 3x + 1$

1. Substitute $x = 1$: $3(1) + 1 = 3 + 1 = 4$

2. Substitute $y = 4$: $4 \geq 4$

Since $4 = 4$, the inequality $y \geq 3x + 1$ holds true for the point $(1, 4)$.

Conclusion: Yes, the point $(1, 4)$ satisfies the inequality $y \geq 3x + 1$.

Would you like further details or have any questions?

Here are 5 related questions to explore further:

1. How do you determine if a point satisfies a strict inequality, such as $y > 3x + 1$?
2. What is the geometric interpretation of an inequality like $y \geq 3x + 1$ on a graph?
3. Can multiple points satisfy the inequality $y \geq 3x + 1$?
4. How would you check if the point $(0, 0)$ satisfies the inequality $y \geq 3x + 1$?
5. What does the line $y = 3x + 1$ represent in the context of this inequality?

Tip: When testing a point against an inequality, substitute the values into the inequality, and check if the resulting statement is true or false.