In the inequality Y > 2X + 5, what is the smallest integer y-value that satisfies this inequality?

To determine the smallest integer value of ( y ) that satisfies the inequality ( Y > 2X + 5 ), it is important to understand how the inequality defines a region in relation to a line on a graph.

First, rewrite the inequality to isolate ( y ): ( Y > 2X + 5 ). This means that the value of ( Y ) must be greater than ( 2X + 5 ) for any given value of ( X ).

To find the smallest integer ( y )-value, consider what happens when we set ( X = 0 ) (the y-intercept) to simplify evaluation. Plugging ( X = 0 ) into the inequality, we get:

[

Y > 2(0) + 5 \implies Y > 5

]

This tells us that for ( X = 0 ), any ( y )-value must be greater than 5. The smallest integer that fulfills this condition is 6.

If we assess higher values for ( X ), we’ll find that as ( X ) increases, ( 2X + 5 ) will also increase. However, since the question asks for