Question

the scatter plot shows the total number of computer games anna played and the scores she earned. part a what is the equation of the linear model using two points on the line? y = x + 1 y = x - 1 y = -x + 1 y = -x - 1 part b select all the patterns that correctly describe the graph. linear association non - linear association strong positive correlation strong negative correlation no correlation

Explanation:

Step1: Find the slope of the line

Take two points on the line, say \((1,2)\) and \((3,4)\).
The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the values: \(m=\frac{4 - 2}{3 - 1}=\frac{2}{2}=1\).

Step2: Find the y - intercept

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((1,2)\) and \(m = 1\).
\(y-2=1\times(x - 1)\)
\(y-2=x - 1\)
\(y=x+1\)

For Part B:
Since there is a line of best fit (linear model), it shows a linear association. As the slope of the line is positive (\(m = 1>0\)), the points are clustered around the line (though not perfectly), so there is a strong positive correlation.

Answer:

Part A: \(y=x + 1\)
Part B: linear association, strong positive correlation