Graphing data Knowledge-Based Practice

Questions

1. 1.

   Which graphical feature confirms that two physical quantities have a directly proportional relationship?

   • A) A straight best-fit line that passes through the origin
   • B) A curved best-fit line that levels off horizontally
   • C) A straight best-fit line with a positive non-zero vertical intercept
   • D) A horizontal best-fit line across all measured data points
2. 2.

   When interpreting a linear graph of experimental data in physics, what does the vertical intercept represent?

   • A) The estimated value of the dependent variable when the independent variable is zero
   • B) The constant rate of change of the dependent variable per unit change in the independent variable
   • C) The ratio of the dependent variable to the independent variable across all recorded data points
   • D) The point where the experimental uncertainty of the measurements reaches its minimum value
3. 3.

   When analyzing experimental data displayed on a graph, which statement correctly describes the process of interpolation?

   • A) Estimating a value that falls outside the range of recorded data points.
   • B) Adjusting the axes so that the line of best fit passes directly through the origin.
   • C) Estimating an unknown value that lies between already collected data points.
   • D) Calculating the rate of change by dividing the vertical rise by the horizontal run.
4. 4.

   When plotting experimental data that exhibit measurement scatter, why is a best-fit line drawn rather than connecting the data points dot-to-dot?

   • A) Connecting points directly is only valid when measuring quantities that have zero experimental uncertainty.
   • B) Connecting points dot-to-dot alters the original numerical coordinates recorded in the data table.
   • C) A best-fit line smooths out random experimental uncertainties to reveal the underlying relationship between the variables.
   • D) A best-fit line ensures that the plotted curve passes directly through the origin to satisfy physical laws.
5. 5.

   When establishing the numerical scale along an axis of a standard graph for experimental data, which rule must be followed?

   • A) Each recorded data value should be written directly at consecutive tick marks along the axis.
   • B) The numerical interval between consecutive tick marks should change according to where data points cluster.
   • C) Equal spatial intervals along an axis must represent equal numerical increments of the plotted quantity.
   • D) Both the horizontal and vertical axes must always share identical numerical intervals between grid lines.
6. 6.

   When determining the slope of a linear relationship from an experimental graph, which method should be used?

   • A) Divide the vertical coordinate of any single recorded data point by its horizontal coordinate.
   • B) Use the coordinates of the first and last measured data points from the experimental table.
   • C) Calculate the average of all recorded data points and compute the ratio between their sums.
   • D) Select two widely spaced points directly on the drawn line of best fit rather than original data points.
7. 7.

   When constructing a line graph to represent experimental data in a physics investigation, which convention should be followed when assigning variables to the axes?

   • A) The dependent variable is placed on the horizontal axis ($x$-axis), and the independent variable is placed on the vertical axis ($y$-axis).
   • B) The independent variable is placed on the horizontal axis ($x$-axis), and the dependent variable is placed on the vertical axis ($y$-axis).
   • C) Both variables are placed together on the vertical axis ($y$-axis) while time is automatically assigned to the horizontal axis.
   • D) The variable with the larger numerical range is placed on the horizontal axis ($x$-axis), regardless of which variable was manipulated.

Answers and step-by-step solutions appear after you finish the test.