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

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

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

Answer 1

To determine whether the point \( (0, -3) \) is a solution to the inequality \( y > 45x - 3 \), we need to analyze the graph of the inequality.

1. Understanding the Boundary Line: The boundary line for the equation \( y = 45x - 3 \) is dashed, indicating that points on the line do not satisfy the inequality (the inequality is greater than, not greater than or equal to).

2. Evaluating the Point: The point \( (0, -3) \) corresponds to \( x = 0 \) and \( y = -3 \). To see if this point satisfies the inequality, we will substitute \( x = 0 \) into the equation of the boundary line: \[ y = 45(0) - 3 \Rightarrow y = -3. \] Thus, the point \( (0, -3) \) lies on the boundary line.

3. Shading: According to the provided description, the shading extends from the line to the left. Therefore, the region to the left of the line includes points where \( y \) is less than \( 45x - 3 \).

Now that we have this information, we can conclude:

• Since \( (0, -3) \) lies on the dashed boundary line, it does not satisfy the inequality \( y > 45x - 3 \).

Therefore, the correct response is:

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