Question

which equation could represent the line of best fit for this data? y = -\frac{1}{4}x + 20 y = -\frac{1}{2}x + 40 y = 2x + 12 y = -x + 36 y = x + 10 y = 4x + 8

Explanation:

Step1: Observe the trend of data points

The data points show a positive - slope trend as the value of \(x\) increases, the value of \(y\) also increases. So, we can rule out equations with negative slopes (\(y =-\frac{1}{4}x + 20\), \(y=-\frac{1}{2}x + 40\), \(y=-x + 36\)).

Step2: Estimate the slope and y - intercept

By looking at the data points, when \(x = 0\), the \(y\) - value of the line of best fit seems to be around 10 - 12. And the slope of the line of best fit should be positive. Among the remaining positive - slope equations (\(y = 2x+12\), \(y=x + 10\), \(y = 4x+8\)), if we consider the general position of the points, the line \(y=x + 10\) seems to fit the data better. When \(x = 6\), for \(y=x + 10\), \(y=16\); when \(x = 12\), \(y = 22\) which is more in line with the general trend of the data points compared to the other positive - slope equations.

Answer:

\(y=x + 10\)