Question

1. which equation could represent a possible trend line for the data in the scatter plot?

a) ( y = - 2x + 1 ) b) ( y = 2x + 1 )
c) ( y = - 2x - 1 ) d) ( y = 2x - 1 )

Explanation:

Step1: Determine the slope sign

As \(x\) increases, \(y\) increases. So the slope \(m>0\).
For \(y = - 2x+1\), \(m=-2<0\); for \(y=-2x - 1\), \(m = - 2<0\). We can rule out options a) and c).

Step2: Estimate the \(y\) - intercept

When \(x = 0\), from the scatter - plot, the \(y\) value is around \(y = 1\).
For the equation \(y=2x + 1\), when \(x = 0\), \(y=2\times0 + 1=1\). For the equation \(y = 2x-1\), when \(x = 0\), \(y=2\times0-1=-1\).

Answer:

B. \(y = 2x + 1\)