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

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.

1 answer

To determine if the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we can start by checking where the point falls in relation to the boundary line defined by the equation \( y = \frac{4}{5}x - 3 \).

  1. Substitute x = 0 into the boundary line equation: \[ y = \frac{4}{5}(0) - 3 = -3 \] This means that when \( x = 0 \), \( y = -3 \), which is the exact boundary point (0, -3).

  2. Analyze the inequality: The inequality \( y > \frac{4}{5}x - 3 \) indicates that the area above the line is included but not the line itself. Since (0, -3) is exactly on the line, it does not satisfy the inequality because it does not fulfill the condition of being greater than the value on the line.

Given this analysis, the correct response is:

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