Question

Is the point (0,−3) a solution to the inequality y>4/5x−3 , as shown on the graph?

(1 point)
Responses

Yes, because (0,−3) falls within the shaded region.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.

Yes, because (0,−3) falls on the boundary line.
Yes, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.

No, because (0,−3) falls on the boundary line.
No, because left parenthesis 0 comma negative 3 right parenthesis falls on the boundary line.

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

Answer 1

To determine whether the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we can first substitute the x-coordinate of the point into the equation of the boundary line:

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

This means that the point (0, -3) lies on the boundary line \( y = \frac{4}{5}x - 3 \).

2. The inequality \( y > \frac{4}{5}x - 3 \) indicates that \( y \) must be greater than \(-3\) when \( x = 0\).

Since \( -3 \) is not greater than \(-3\), the point (0, -3) does not satisfy the inequality \( y > \frac{4}{5}x - 3 \).

Therefore, the correct answer is:
**No, because (0,−3) falls on the boundary line.**