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: Determine line style

For inequalities with $<$ or $>$, the boundary line is dashed. Here, the inequality is $y < 2x+3$, so the line $y=2x+3$ is dashed.

Step2: Determine shading region

To find the shaded area, test a 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.