Question

which of the following equations best represents this line of best fit?
a $y = 1.54x$
b $y = 10.38 - 1.54x$
c $y = 10.38$
d $y = - 10.38x$
question 7 of 22

Explanation:

Step1: Determine the slope type

The line of best fit is decreasing, so the slope \(m\) is negative. Option A (\(y = 1.54x\), \(m=1.54>0\)) and Option C (\(y = 10.38\), \(m = 0\)) and Option D (\(y=-10.38x\), when \(x = 1\), \(y=-10.38\) which is not in line with the graph's \(y\)-intercept around \(y = 10\)) can be preliminarily eliminated.

Step2: Use the slope - intercept form \(y=mx + b\)

The general form of a line is \(y=mx + b\), where \(b\) is the \(y\)-intercept. From the graph, when \(x = 0\), \(y\approx10\). For the line \(y=10.38-1.54x\), when \(x = 0\), \(y = 10.38\) (close to the observed \(y\)-intercept from the graph). And the slope \(m=-1.54\) (negative, consistent with the decreasing trend of the line of best fit).

Answer:

B. \(y = 10.38-1.54x\)