Question

Which of the following points is a solution to the linear inequality y>19x−29
?(1 point)
Responses

(0,−13)
left parenthesis 0 comma negative Start Fraction 1 over 3 End Fraction right parenthesis

(0,−19)
left parenthesis 0 comma negative Start Fraction 1 over 9 End Fraction right parenthesis

(0,−49)
left parenthesis 0 comma negative Start Fraction 4 over 9 End Fraction right parenthesis

(0,−29)

Answer 1

To determine which of the given points is a solution to the linear inequality \( y > 19x - 29 \), we need to evaluate each point by substituting \( x \) into the inequality and seeing if the corresponding \( y \) value satisfies it.

The inequality can be simplified for \( x = 0 \):

\[
y > 19(0) - 29 \implies y > -29
\]

This means any point with \( y \) greater than \(-29\) will satisfy the inequality when \( x = 0\). Now, let's analyze the provided points:

1. \((0, -13)\): \( -13 > -29\) (satisfies the inequality)
2. \((0, -\frac{1}{3})\): \(-\frac{1}{3} > -29\) (satisfies the inequality)
3. \((0, -19)\): \( -19 > -29\) (satisfies the inequality)
4. \((0, -\frac{1}{9})\): \(-\frac{1}{9} > -29\) (satisfies the inequality)
5. \((0, -29)\): \(-29\) is not greater than \(-29\) (does not satisfy the inequality)

Thus, the points that satisfy the inequality \( y > 19x - 29 \) for \( x = 0\) are:

- (0, -13)
- (0, -\frac{1}{3})
- (0, -19)
- (0, -\frac{1}{9})

The only point that does not satisfy it is (0, -29).

In conclusion, the points \((0, -13)\), \((0, -\frac{1}{3})\), \((0, -19)\), and \((0, -\frac{1}{9})\) are all solutions, while \((0, -29)\) is **not** a solution.