When graphing the inequality y > x + 3, where is the shading placed relative to the boundary line?

When graphing the inequality y > x + 3, where is the shading placed relative to the boundary line?

• A. Not determined
• B. Below the line
• C. Above the line
• D. On the line

Answer: (C)

For the inequality y > x + 3, think of the line y = x + 3 as the boundary where the two sides meet. The inequality asks for all points whose y-coordinate is greater than the line's value at the same x, so the solution region is the area above that boundary line. Because the inequality is strict, points on the line itself do not satisfy it, so the line would be drawn with dashed style and the shading sits above. A quick check: take a point above the line, such as (0,4). Here 4 > 0 + 3 is true, so this point belongs in the shaded region. A point below, like (0,2), would give 2 > 3, which is false, so it’s not shaded.

For the inequality y > x + 3, think of the line y = x + 3 as the boundary where the two sides meet. The inequality asks for all points whose y-coordinate is greater than the line's value at the same x, so the solution region is the area above that boundary line. Because the inequality is strict, points on the line itself do not satisfy it, so the line would be drawn with dashed style and the shading sits above. A quick check: take a point above the line, such as (0,4). Here 4 > 0 + 3 is true, so this point belongs in the shaded region. A point below, like (0,2), would give 2 > 3, which is false, so it’s not shaded.