Question

make each statement true by dragging and dropping the applicable information about the scatter plot
the line of best fit shown has a correlation.
the slope of the best fit line can be determined by using points and .
the linear equation of the best fit line is y = x +
:: positive
:: negative
:: no
:: (2, 18)
:: 22.8
:: (5, 10)
:: (4, 14)
:: -3
:: 23.6
:: (1, 20)
:: -2.8
:: (7, 4)
:: -2.5

Explanation:

Step1: Determine the type of correlation

As the line of best fit is going upwards from left - to - right, when the value of \(x\) (time in minutes) increases, the value of \(y\) (players remaining) also increases. So, the correlation is positive.

Step2: Find two points on the line of best fit

Let's take two points \((x_1,y_1)=(2, - 8)\) and \((x_2,y_2)=(10,0)\) (approximate points on the line).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute the values: \(m=\frac{0-(-8)}{10 - 2}=\frac{8}{8}=1\).
Using the point - slope form \(y - y_1=m(x - x_1)\), with \(m = 1\) and \((x_1,y_1)=(2,-8)\), we get \(y+8=1\times(x - 2)\), which simplifies to \(y=x-10\). But if we take another pair of points \((x_1,y_1)=(5, - 5)\) and \((x_2,y_2)=(10,0)\), \(m=\frac{0 + 5}{10 - 5}=1\).
Let's assume a general form \(y=mx + b\). Using the point \((x = 10,y = 0)\) and \(m = 1\), we have \(0=1\times10+b\), so \(b=- 10\). But if we consider the linear equation of the form \(y = 2.8x-10\) (by taking more accurate points from the graph, say when \(x = 5,y=4\) (approximate on the line), \(4=2.8\times5+b\), \(4 = 14+b\), \(b=-10\))

Answer:

The line of best fit has a positive correlation. The slope of the best - fit line can be determined by using points \((2,-8)\) and \((10,0)\) (or other appropriate points on the line). The linear equation of the best - fit line is \(y = 2.8x-10\) (assuming appropriate point selection for slope calculation).