Question
Is the point
(0,-3) a solution to the inequality y>4/5x-3, as shown on the graph?(1 point)
A: No, because (0,-3) falls within the shaded region.
B: Yes, because (0,-3) falls within the shaded region.
C: No, because (0,-3) falls on the boundary line.
D: Yes, because (0,-3) falls on the boundary line.
(0,-3) a solution to the inequality y>4/5x-3, as shown on the graph?(1 point)
A: No, because (0,-3) falls within the shaded region.
B: Yes, because (0,-3) falls within the shaded region.
C: No, because (0,-3) falls on the boundary line.
D: Yes, because (0,-3) falls on the boundary line.
Answers
GPT-4o mini
To determine if the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we first substitute \( x = 0 \) into the equation of the boundary line:
\[
y = \frac{4}{5}(0) - 3 = -3
\]
This means the point (0, -3) lies on the boundary line of the inequality.
The inequality \( y > \frac{4}{5}x - 3 \) indicates that we are looking for points where \( y \) is greater than the value given by the line. Since (0, -3) is equal to the value on the boundary line, it does not satisfy the inequality because the inequality is strict (greater than, not greater than or equal to).
Given this analysis, the correct answer is:
**C: No, because (0,-3) falls on the boundary line.**
\[
y = \frac{4}{5}(0) - 3 = -3
\]
This means the point (0, -3) lies on the boundary line of the inequality.
The inequality \( y > \frac{4}{5}x - 3 \) indicates that we are looking for points where \( y \) is greater than the value given by the line. Since (0, -3) is equal to the value on the boundary line, it does not satisfy the inequality because the inequality is strict (greater than, not greater than or equal to).
Given this analysis, the correct answer is:
**C: No, because (0,-3) falls on the boundary line.**