Question

You have the following data points which belong to a function of the form , where can be positive or negative.

4.11 6.27 9.57
0.100 0.200 0.300
You wish to determine the value of the constant, , and to do so you will construct a linear plot. What will you plot against what?
-axis label:
-axis label:
From the values of and in the table above, calculate the values of the three corresponding data points. Click on the graph below, and use the "Freeform Curves" tool to plot the data. Line segments will automatically connect the points.
Enter Solution
What is the numerical value of the constant, ?

Answer 1

To determine the constant k for a linear function represented by a set of data points, one should plot the points on a graph, draw a trend line using least-squares regression, and then calculate the slope of this line, which corresponds to k.

Step-by-step explanation:

The student is working with a set of data points and needs to determine the value of a constant for a function, likely of the form f(x) = kx or a similar linear relationship. To find the value of the constant k, the student should plot the given data points on a graph and then determine the slope of the trend line that best fits the data. This can be done by calculating the slope (rise over run) between the different points, or by using a least-squares regression method if using a calculator or specific software.

Once the data is plotted and the best-fit line is drawn, the slope of this line will provide the value of k. If the equation is of the form y = kx, then the slope of the line is k. If the function's formula is slightly different, the method to find k may involve more steps, but the principle remains the same.