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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

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.

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

To determine whether the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we need to analyze the information given.

  1. The inequality \( y > \frac{4}{5}x - 3 \) represents a region above the dashed line.
  2. The dashed line indicates that points on the line are not included in the solution set (since it’s a "greater than" inequality).
  3. The point (0, -3) corresponds to x = 0 and y = -3.

Now, let's check if (0, -3) satisfies the inequality:

  • Substitute x = 0 into the right side of the inequality: \[ y > \frac{4}{5}(0) - 3 \implies y > -3 \]
  • For the point (0, -3), the y-coordinate is -3.

Since -3 is not greater than -3, the point (0, -3) does not satisfy the inequality.

Now, to determine the position of the point relative to the dashed line:

  • The point (0, -3) lies on the dashed line itself since substituting (0, -3) into the equation gives us equality.

Given that the inequality is strict (greater than), and that (0, -3) lies on the boundary (dashed) line, it is not a solution.

Therefore, the appropriate response is: No, because (0, -3) falls on the boundary line.