Use the image to answer the question.

Question

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 within the shaded region.
No, 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.

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

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

Answer 1

To determine whether the point (0, -3) is a solution to the inequality \( y > 45x - 3 \), we need to first evaluate the inequality at the point:

1. Substitute \( x = 0 \) into the inequality: \[ y > 45(0) - 3 \] which simplifies to: \[ y > -3 \]

2. Now we check the y-coordinate of the point (0, -3): \[ -3 > -3 \] This statement is false since -3 is not greater than -3.

From this analysis, the point (0, -3) does not satisfy the inequality \( y > 45x - 3 \).

Next, consider where the point falls in relation to the graph. The dashed line representing \( y = 45x - 3 \) indicates that points on this line are not included in the solution (since the inequality is strictly greater than, not greater than or equal to). Since (0, -3) lies exactly on this line, we conclude:

The correct answer is:

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