A Line Splits the Plane

An equation like $y = x+1$ has a line as its graph. Change the = to < and the solutions are no longer a line. They fill a whole region. The solutions of $y < x+1$ are all the points below the line $y = x+1$. At every point below the line, the y-coordinate is smaller than $x+1$.

The solutions of y < x + 1 are all the points below the line

The equation gives the boundary line. Once y is isolated on the left, $y > mx+b$ shades above the line and $y < mx+b$ shades below it. The inequality describes all points in that half-plane.