The number line you described shows a closed circle at 1, indicating that 1 is included in the solution, and a line extending toward 10 with an arrow, indicating that the values greater than 1 are included in the solution but not including 10.
This can be expressed as the inequality:
\[ x \geq 1 \]
So, the linear inequality that is graphed on the number line is \( x \geq 1 \).