Doesthepoint(1, 4)satisfytheinequalityy ≥ 3x + 1?


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.

Does the point (1, 4) satisfy the inequality y ≥ 3x + 1?

Learn how to determine if the point (1, 4) satisfies the inequality y ≥ 3x + 1. This solution uses substitution to verify whether the inequality holds, covering key concepts in algebra and coordinate geometry. Ideal for students in Grades 7-9.

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