The remaining battery percentage, $p$, of a smartphone is affected by the hours of video playback, $h$. Which variable is the dependent variable in this situation?

The remaining battery percentage, $p$.

The hours of video playback, $h$.

A chef notes the final temperature of a soup, $T$, depends on how many minutes it simmers, $m$. A student argues that $m$ is dependent because the chef chooses $m$ based on the target $T$. Which statement is true?

The simmering time, $m$, is the dependent variable because the chef chooses it.

The soup's temperature, $T$, is the independent variable because it's the goal.

The simmering time, $m$, is the independent variable because it causes the temperature to change.

Both $T$ and $m$ are independent variables.

2-1 Representing Relations Practice — Grade 9 math

2-1 Representing Relations — Practice Questions

1. A streaming plan's monthly cost, $c$, depends on the number of screens, $s$, allowed. In this relationship, the number of screens, $s$, is the ___ variable. (enter "independent" or "dependent")
2. The remaining battery percentage, $p$, of a smartphone is affected by the hours of video playback, $h$. Which variable is the dependent variable in this situation?
- A. The remaining battery percentage, $p$.
- B. The hours of video playback, $h$.
- C. Both $p$ and $h$.
- D. Neither $p$ nor $h$.
3. The total time, $T$, it takes to fill a swimming pool depends on the pool's volume, $V$, and the flow rate of the hose, $R$. The pool's volume, $V$, is an ___ variable. (enter "independent" or "dependent")
4. A chef notes the final temperature of a soup, $T$, depends on how many minutes it simmers, $m$. A student argues that $m$ is dependent because the chef chooses $m$ based on the target $T$. Which statement is true?
- A. The simmering time, $m$, is the dependent variable because the chef chooses it.
- B. The soup's temperature, $T$, is the independent variable because it's the goal.
- C. The simmering time, $m$, is the independent variable because it causes the temperature to change.
- D. Both $T$ and $m$ are independent variables.
5. The resale value of a textbook, $v$, decreases based on its age in years, $y$. In this relationship, the resale value, $v$, is the ___ variable. (enter "independent" or "dependent")
6. A relation contains $\{(10, 3),\ (20, 6),\ (30, 9),\ (40, 12)\}$. Which scale is most appropriate for the $x$-axis?
- A. 1 unit per grid square
- B. 5 units per grid square
- C. 10 units per grid square
- D. 50 units per grid square
7. A relation includes the point $(-5, 12)$. Where should the origin be placed on the coordinate plane to display this point?
- A. At the lower-left corner only
- B. Centered so that $x = -5$ is visible on the left side of the $x$-axis
- C. At the upper-right corner
- D. The origin does not need to be shown
8. A relation contains $\{(500, 10),\ (1000, 20),\ (1500, 30)\}$. To avoid wasting space, the $x$-axis should begin at $x =$ ___ rather than at $0$.
9. A relation has $y$-values ranging from $0$ to $150$. Which $y$-axis scale best spreads the points across a 10-square grid without leaving large empty regions?
- A. 1 unit per grid square
- B. 5 units per grid square
- C. 15 units per grid square
- D. 100 units per grid square
10. A relation contains $\{(-4, -8),\ (-2, -4),\ (0, 0),\ (2, 4)\}$. Which statement best describes the appropriate axis setup?
- A. Place the origin at the lower-left corner since all values are small
- B. Center the axes so both negative $x$- and $y$-values are visible
- C. Use only the positive quadrant since the relation passes through the origin
- D. Start the $x$-axis at $x = 2$ to save space