Question

use the points to describe the data and determine the line of best fit.
what type of correlation do the data points represent?
negative
what is the best estimate for the y - intercept?

what is the equation that best represents the data?

Explanation:

Step1: Determine the y - intercept

Looking at the scatter plot, when \(x = 0\) (extrapolating the trend of the line of best fit), the \(y\) - value (elevation) is around \(1600\).

Step2: Find the equation of the line

We know the general form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
Since the correlation is negative, the slope \(m\) is negative.
Let's assume two points to estimate the slope. For example, if we take a point around \((20,1200)\) and \((60,600)\)
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{600 - 1200}{60 - 20}=\frac{- 600}{40}=-15\)
The \(y\) - intercept \(b = 1600\)
So the equation of the line is \(y=-15x + 1600\)

Answer:

The best estimate for the \(y\) - intercept is \(1600\). The equation that best represents the data is \(y=-15x + 1600\)