Question

given the graph of a scatterplot and a trend line, explain how you would find the equation of the trend line. sample response: to determine the equation, identify two points on the trend line. calculate the slope between the two points. use the slope - intercept form with the slope and one of the points from the line to determine the y - intercept. write the equation with the slope and the y - intercept. which did you include in your explanation? check all that apply. calculate the slope of the line through the two points. identify two points on the trend line. substitute the slope and a point on the trend line into the slope - intercept equation and solve for the y - intercept. substitute the slope and y - intercept for m, and b for the slope - intercept form.

Explanation:

To find the equation of the trend line, first identify two points on it. Then calculate the slope using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Next, use the slope - intercept form \(y = mx + b\) with the slope and one of the points to solve for the \(y\) - intercept \(b\). Finally, write the equation with the found slope \(m\) and \(y\) - intercept \(b\). All the given options are part of this process.

Answer:

All of the options: "Calculate the slope of the line through the two points", "Identify two points on the trend line", "Substitute the slope and a point on the trend line into the slope - intercept equation and solve for the \(y\) - intercept", "Substitute the slope and \(y\) - intercept for \(m\), and \(b\) for the slope - intercept form" should be included.