Ask a New Question
Menu

Use the image to answer the 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.

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 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.

1 answer

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

  1. The boundary line for the inequality \( y = 45x - 3 \) is dashed, indicating that points on the line are not included in the solution set for the inequality \( y > 45x - 3 \).
  2. The region shaded is to the left of this line, which represents the values of \( y \) that are greater than \( 45x - 3 \).

Now, let's check the point (0, -3):

  • Substitute \( x = 0 \) into the inequality:

    \( y > 45(0) - 3 \)
    \( y > -3 \)

Here, when \( x = 0 \), we have \( y > -3 \). The point (0, -3) has \( y = -3 \), which is not greater than -3. Therefore, (0, -3) does not satisfy the inequality.

Since (0, -3) falls exactly on the boundary line, and the line is dashed, it confirms that:

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