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>45x−3
, as shown on the graph?

(1 point)
Responses

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.
No, because left parenthesis 0 comma negative 3 right parenthesis falls within the shaded region.

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.
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Answer 1

To determine whether the point (0, -3) is a solution to the inequality \( y > 4.5x - 3 \), we can analyze the given information.

1. The line in the inequality acts as a boundary; since it is dashed, points on the line do not satisfy the inequality.
2. The shaded region extends to the left of this dashed line, which indicates that the inequality is satisfied by points in that region (i.e., points where \( y \) is greater than \( 4.5x - 3 \)).

Now, let's plug in the coordinates of the point (0, -3) into the equation of the boundary line:

• For \( x = 0 \): \[ y = 4.5(0) - 3 = -3 \] Thus, the point (0, -3) lies exactly on the boundary line.

Since the line is dashed, (0, -3) does not satisfy the inequality \( y > 4.5x - 3 \), meaning it is not part of the solutions for this inequality.

So the correct response is:

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