Integers — number line and all operations

On the number line, numbers increase as you move to the right. The further left a number is, the smaller it is. So the most negative number is the smallest.

Placing them on the number line from left to right: $-8$ is furthest left, then $-5$, then $-2$, then $0$, then $1$, then $3$ is furthest right.

Reading from left to right gives the order from smallest to largest: $-8,-5,-2,0,1,3$.

We need the integers arranged from smallest to largest, meaning the most negative first and the most positive last.

The smallest integer must be $-8$ (furthest left on the number line). The option '$-2,-5,-8,0,1,3$' starts with $-2$, which is not the smallest, so eliminate it.

The option '$3,1,0,-2,-5,-8$' goes from largest to smallest — the opposite of what is asked. Eliminate it.

The option '$-8,-5,-2,1,0,3$' places $0$ after $1$, but $0<1$, so $0$ should come before $1$. Eliminate it.

The remaining option '$-8,-5,-2,0,1,3$' correctly orders all integers from smallest to largest.

The diver starts at $-15$ m. Ascending means moving right (adding), and descending means moving left (subtracting). The expression is $-15+6-10$.

First, $-15+6=-9$. Then, $-9-10=-19$.

The diver's final depth is $-19$ m, meaning 19 m below sea level.

Start: $-15$ m. Ascending 6 m adds 6. Descending 10 m subtracts 10. The net change is $+6-10=-4$.

The option $11$ m is positive, meaning above sea level. Starting at $-15$ m and making a net change of $-4$ cannot give a positive result. Eliminate $11$ m.

The option $-1$ m would require a net change of $+14$, but we calculated a net change of $-4$. Eliminate $-1$ m. The option $-31$ m would require a net change of $-16$, which is also wrong. Eliminate $-31$ m.

$-15+(-4)=-19$ m, so the correct answer is $-19$ m.