To determine which of the points is a solution to the linear inequality \( y > 19x - 29 \), we can substitute the x-coordinate of each point into the inequality and see if the y-coordinate satisfies it.
The inequality we are working with is \( y > 19x - 29 \).
Since all the given points have \( x = 0 \), we can simplify the inequality by substituting \( x = 0 \):
\[ y > 19(0) - 29 \ y > -29 \]
Now we will check each point to see if it satisfies \( y > -29 \):
-
Point (0, -13):
\(-13 > -29\) (True) -
Point (0, -\(\frac{1}{3}\)):
\(-\frac{1}{3} > -29\) (True) -
Point (0, -19):
\(-19 > -29\) (True) -
Point (0, -\(\frac{1}{9}\)):
\(-\frac{1}{9} > -29\) (True) -
Point (0, -49):
\(-49 > -29\) (False) -
Point (0, -29):
\(-29 > -29\) (False, because it is not greater)
Now, the points that satisfy the inequality \( y > -29 \) are:
- (0, -13)
- (0, -\(\frac{1}{3}\))
- (0, -19)
- (0, -\(\frac{1}{9}\))
Thus, any of the following points are solutions to the inequality:
- (0, -13)
- (0, -\(\frac{1}{3}\))
- (0, -19)
- (0, -\(\frac{1}{9}\))
The only point that does not satisfy the inequality is (0, -49) and (0, -29).
So, valid responses to the inequality include (0, -13), (0,-\(\frac{1}{3}\)), (0,-19), and (0,-\(\frac{1}{9}\)).