Question

can any two of the given data points in a scatter plot be used to write an equation for a trend line? explain
choose the correct answer below
a. yes any two of the given data points can be used since every point in the set is valid data.
b. no. the two points must be the first and last data points. using other points will not yield the correct equation
c. no. the two points must be data points on the trend line. if the trend line passes through more than two data points, any two may be used.
d. no. the two points must be on the trend line. these points may or may not be given data points.
e. yes. any two of the given data points can be used since the trend line should pass through or nearly pass through all of the data points

Explanation:

A trend line is a line that shows the general pattern of data in a scatter - plot. To write the equation of a trend line, we use the formula \(y - y_1=m(x - x_1)\) where \(m=\frac{y_2 - y_1}{x_2 - x_1}\). The two points \((x_1,y_1)\) and \((x_2,y_2)\) must lie on the trend line. These points may or may not be the original data points. For example, if we have a scatter - plot of data points that follow a linear trend approximately, the trend line is drawn to best represent the data. The points used to calculate the equation of the trend line are points on the trend line itself, not necessarily the given data points.

Answer:

D. No. The two points must be on the trend line. These points may or may not be given data points.