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

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.

Answer 1

To determine whether the point (0, -3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we can substitute the x-value into the inequality and check if the corresponding y-value satisfies the inequality.

1. Substitute \( x = 0 \) into the equation:
\[
y = \frac{4}{5}(0) - 3 = -3
\]

2. The boundary line of the inequality is represented by \( y = \frac{4}{5}x - 3 \). Since \( y > \) (not \( \geq \)), the line itself is not included in the solution.

3. Now we can compare:
\[
-3 > -3
\]
This is false since -3 is not greater than -3.

Therefore, the point (0, -3) does not satisfy the inequality, and since it falls on the boundary line, the correct choice is:

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