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 a point close to \((0,20)\), so the y - intercept \(b\) is approximately \(20\).

Step2: Analyze the slope

Take two points on the trend line, say \((2,50)\) and \((4,80)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{80 - 50}{4 - 2}=\frac{30}{2}=15\).
The equation of a line is \(y=mx + b\), substituting \(m = 15\) and \(b=20\) gives \(y = 15x+20\).

Answer:

\(y = 15x + 20\)