Is the point (0,−3) a solution to the inequality y4/5x−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.

Question

Is the point (0,−3) a solution to the inequality y>4/5x−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.

GPT-4o mini · Answer

To determine if the point (0,−3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we can first evaluate the inequality at the point.

Substituting \( x = 0 \) into the inequality:

\[ y > \frac{4}{5}(0) - 3 \]

This simplifies to:

\[ y > -3 \]

Now, we check the y-value of the point (0, -3):

\[ -3 > -3 \]

This statement is false.

Since (0, -3) does not satisfy the inequality \( y > \frac{4}{5}x - 3 \), we can conclude that (0, -3) is not a solution to the inequality.

The correct response would be: No, because (0, -3) falls on the boundary line.