Question

Is the point (0, -3) a solution to the inequality y>4/5x−3
, as shown on the graph?
The dashed line has its shaded region on the top left.
(1 point)
Responses

Yes, because (0, -3) falls within the shaded region.
Yes, because (0, -3) falls within the shaded region.

No, because (0, -3) falls within the shaded region.
No, because (0, -3) falls within the shaded region.

No, because (0, -3) falls on the dashed boundary line.
No, because (0, -3) falls on the dashed boundary line.

Yes, because (0, -3) falls on the dashed boundary line.
Yes, because (0, -3) falls on the dashed boundary line.

Answer 1

To determine if the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we can substitute \( x = 0 \) into the inequality:

1. Substitute \( x = 0 \):
\[ y > \frac{4}{5}(0) - 3 \]
\[ y > -3 \]

Now, we check the y-coordinate of the point (0, -3):
- The inequality \( y > -3 \) means that \( y \) must be greater than -3.
- The y-coordinate of the point (0, -3) is -3, which does not satisfy the inequality \( y > -3 \).

Therefore, the point (0, -3) is not a solution to the inequality.

The correct response would be:
**No, because (0, -3) falls on the dashed boundary line.**