Question

Consider the inequality y(>/=)ax+6. The point (2, 1) is in the solution region when

A. a>-(5/2)
B. a<-(5/2)
C. a(>/=)-(5/2)
D. a(</=)-(5/2)

Answer 1

Put x = 2 , y = 1 in inequality

y ≥ a x + 6

1 ≥ a ∙ 2 + 6

1 ≥ 2 a + 6

Subtract 6 to both sides

- 5 ≥ 2 a

Divide both sides by 2

- 5 / 2 ≥ a

This means:

a ≤ - 5 / 2

Answer 2

[AI-generated answer — Explain Bot]

To determine whether the point (2, 1) is in the solution region of the inequality y ≥ ax + 6, we need to substitute the x and y values of the point into the inequality and check if it holds true.

Substituting x = 2 and y = 1 into the inequality:

1 ≥ a(2) + 6

Simplifying the equation:

1 ≥ 2a + 6

Now, let's solve for a.

Subtracting 6 from both sides of the equation:

1 - 6 ≥ 2a

-5 ≥ 2a

Finally, dividing both sides of the equation by 2:

a ≤ -5/2

From our calculations, we find that a must be less than or equal to -5/2 in order for the point (2, 1) to be in the solution region of the inequality.

Therefore, the correct answer is:

C. a ≤ -(5/2)