Question

which of the following equations is the best model for a line of fit for the data?
$hat{y}=-1.34x + 21.5$

Explanation:

Step1: Observe the trend of data points

The data points show a negative - linear trend, meaning as the money saved (x - variable) increases, the money earned (y - variable) decreases.

Step2: Recall the slope - intercept form of a line

The equation of a line is $\hat{y}=mx + b$, where $m$ is the slope and $b$ is the y - intercept. A negative slope ($m<0$) indicates a decreasing trend.

Step3: Analyze the given equation

The equation $\hat{y}=-1.34x + 21.5$ has a negative slope ($m=-1.34$) which is consistent with the negative trend of the data points.

Answer:

$\hat{y}=-1.34x + 21.5$