Question

the scatterplot shows the relationship between two variables, x and y, for data set e. a line of best fit is shown. data set f is created by multiplying the y - coordinate of each data point from data set e by 3.9. which of the following could be an equation of a line of best fit for data set f? a) y = 46.8 + 5.9x b) y = 46.8 + 1.5x c) y = 12 + 5.9x d) y = 12 + 1.5x

Explanation:

Step1: Recall the effect of multiplying y - values

When we multiply the y - coordinates of all data points by a constant \(k = 3.9\), the y - intercept and the slope of the line of best - fit will also be multiplied by \(k\). First, estimate the equation of the line of best - fit for data set E in the form \(y=mx + b\). The y - intercept \(b\) of the line of best - fit for data set E is around \(b_E\approx12\) and the slope \(m_E\) can be estimated using two points. Let's take two points \((0,12)\) and \((20,45)\). The slope \(m_E=\frac{45 - 12}{20-0}=\frac{33}{20}=1.65\approx1.5\).

Step2: Calculate the new y - intercept and slope for data set F

The new y - intercept \(b_F\) for data set F is \(b_F=3.9\times b_E\). Since \(b_E\approx12\), then \(b_F = 3.9\times12=46.8\). The new slope \(m_F\) for data set F is \(m_F=3.9\times m_E\). Since \(m_E\approx1.5\), then \(m_F=3.9\times1.5 = 5.85\approx5.9\).

Answer:

A. \(y = 46.8+5.9x\)