Use the image to answer the question.

Question

A coordinate plane shows a graph of an upward-sloping, diagonal, dashed line, with shading extending from the line to the left. The line starts in quadrant 3, extends through quadrant 4, and ends in quadrant 1.

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 need to analyze its relationship to the boundary line represented by the equation \( y = \frac{4}{5}x - 3 \).

1. First, we can check whether the point (0,−3) lies on the boundary line. To do this, we substitute \( x = 0 \) into the equation:

   \[ y = \frac{4}{5}(0) - 3 = -3 \]

   Since the calculated value of \( y \) equals -3, the point (0,−3) does indeed lie on the boundary line.

2. Next, we need to consider the direction of the inequality \( y > \frac{4}{5}x - 3 \). The inequality indicates that we are looking for points where \( y \) is greater than the value of the boundary line.

Since (0,−3) lies exactly on the boundary line, it does not satisfy the condition \( y > \frac{4}{5}x - 3 \).

Therefore, the correct response is:

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