Is the point (0,−3) a solution to the inequality y45x−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. 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.

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 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. 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.

GPT-4o mini · Answer

To determine whether the point (0, -3) is a solution to the inequality \( y > 45x - 3 \), we first need to check where the point (0, -3) lies in relation to the boundary line given by the equation \( y = 45x - 3 \).

Substitute \( x = 0 \) into the equation: \[ y = 45(0) - 3 = -3. \] This means that the boundary line passes through the point (0, -3).
Since this is an inequality \( y > 45x - 3 \), the boundary line \( y = 45x - 3 \) is not included in the solution set. Therefore, points on the line do not satisfy the inequality.

Given that (0, -3) falls on the boundary line of the inequality (and not above it), the correct response would be:

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