Question

writing the equation of a trend line
blue moon steakhouse
the scatterplot shows how much time diners at the
blue moon steakhouse spend eating their meals
compared to the number of guests in their parties.
which equation best represents the trend line for the
data?
$y = 12x$
$y = 20x$
$y = 15x + 20$
$y = 20x + 40$

Explanation:

Step1: Analyze the y - intercept

The trend line passes through the origin \((0,0)\) (since when \(x = 0\), \(y=0\) for the line of best - fit in the scatter - plot). In the equation \(y=mx + b\), \(b = 0\).

Step2: Estimate the slope

Take two points on the trend line. For example, when \(x = 5\), \(y\approx60\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(5,60)\), \(m=\frac{60 - 0}{5-0}=12\)

Answer:

\(y = 12x\)