Which of the following points is a solution to the linear inequality y>1/9x−2/9 ?(1 point)

Question

Responses

(0,−19)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis

(0,−2/9)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis

(0,−1/3)
left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis

(0,−4/9)

Answer 1

To determine which of the given points is a solution to the inequality $y>\frac{1}{9}x-\frac{2}{9}$, we can substitute the x-coordinate of each point into the equation and check if the resulting y-value is greater than the corresponding value calculated from the inequality.

The inequality can be rewritten as: $$y>\frac{1}{9}x-\frac{2}{9}$$

Since all the points have $x=0$, we substitute $x=0$ into the inequality:

$$y>\frac{1}{9}(0)-\frac{2}{9}$$ $$y>-\frac{2}{9}$$

Now we check each point:

1. (0, -19): $-19>-\frac{2}{9}$ → False (Not a solution)

2. (0, -2/9): $-\frac{2}{9}>-\frac{2}{9}$ → False (Not a solution; note it should be greater, not equal)

3. (0, -1/3): $-\frac{1}{3}>-\frac{2}{9}$ →

   • Convert to a common denominator (9): $-\frac{1}{3}=-\frac{3}{9}$
   • Therefore, $-\frac{3}{9}>-\frac{2}{9}$ → False (Not a solution)

4. (0, -4/9): $-\frac{4}{9}>-\frac{2}{9}$ → False (Not a solution)

None of the given points satisfy the inequality $y>\frac{1}{9}x-\frac{2}{9}$.

Please double-check the inequality or the points provided.