Question

consider the function ( y < 2x + 3 ), which of the following is true?
the line would be solid with shading below.
the line would be dashed with shading above.
the line would be solid with shading above.
the line would be dashed with shading below.

Explanation:

Step1: Identify line style

For inequalities with $<$ or $>$, the boundary line is dashed (since points on the line are not included in the solution set).

Step2: Determine shading direction

To test shading, pick a test point not on the line, e.g., $(0,0)$. Substitute into $y < 2x + 3$:
$0 < 2(0) + 3$ simplifies to $0 < 3$, which is true. Since $(0,0)$ lies below the line $y=2x+3$, the region below the line is shaded.

Answer:

The line would be dashed with shading below.