Which of the following points is a solution to the linear inequality y>19x−29

Question

?(1 point)
Responses

(0,−29)
left parenthesis 0 comma negative Start Fraction 2 over 9 End Fraction right parenthesis

(0,−49)
left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis

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

(0,−13)

Answer 1

To determine which point is a solution to the inequality $y>19x-29$, we will substitute the $x$ values of the points into the inequality and check if the resulting inequality holds true for the corresponding $y$ values.

1. For the point $(0,-29)$: $$y>19(0)-29⟹-29>-29\text{(False)}$$

2. For the point $(0,-\frac{2}{9})$: $$y>19(0)-29⟹-\frac{2}{9}>-29\text{(True)}$$

3. For the point $(0,-49)$: $$y>19(0)-29⟹-49>-29\text{(False)}$$

4. For the point $(0,-\frac{4}{9})$: $$y>19(0)-29⟹-\frac{4}{9}>-29\text{(True)}$$

5. For the point $(0,-19)$: $$y>19(0)-29⟹-19>-29\text{(True)}$$

6. For the point $(0,-\frac{1}{9})$: $$y>19(0)-29⟹-\frac{1}{9}>-29\text{(True)}$$

7. For the point $(0,-13)$: $$y>19(0)-29⟹-13>-29\text{(True)}$$

From this analysis, the following points are solutions to the inequality $y>19x-29$:

• $(0,-\frac{2}{9})$
• $(0,-\frac{4}{9})$
• $(0,-19)$
• $(0,-\frac{1}{9})$
• $(0,-13)$

Out of the options given, the only point that clearly holds true as a direct response is:

• $(0,-\frac{4}{9})$ But also any of the other direct points also work correctly: $(0,-19)$ or $(0,-13)$.

The best conclusive response in this case comes down to the verification that the points (0, -2/9), (0, -19), (0, 0.11) show the correct data.