Question

A set of points is shown on the graph.

Scatter plot with a point at negative 3 comma 9, a point at 0 comma 5, a point at 1 comma 8, a point at 6 comma 7, and a point at 8 comma 3.

Which of the following equations is the best model for a line of fit for the data?

y equals 2 thirds times x plus 7
y equals negative 2 thirds times x plus 7
y equals 1 third times x plus 7
y equals negative 1 third times x plus 7

Answer 1

`\textsf{D)} \quad y =-(1)/(3)x+7`

Explanation:

The line of best fit of a scatter plot is a straight line that represents the general trend or pattern. It should pass as close as possible to the majority of the data points, minimizing the overall distance between the line and the points.

From observation of the given scatter plot, the line shows a negative association. Therefore, the slope of the line is negative. This means we can immediately discount the equations with positive slopes.

If we plot the line with the slope -2/3 (attachment 1 - blue line), we can see that the line passes through the first point, then has 3 points above the line but only 1 point below it. The distance between point (6, 7) and the line is much greater than the distance between the line and the other points.

If we plot the line with the slope -1/3 (attachment 2 - red line), we can see that the line passes as close as possible to the majority of the data points, and minimizes the overall distance between the line and the points.

Therefore, the equation that is the best model for the line of best fit for the data is:

`y =-(1)/(3)x+7`