Question

which equation could represent the line of best fit for this data? y = 1/4x + 4 y = 1/6x + 10 y = -3x + 9 y = -4x + 8 y = 1/3x + 8 y = -6x + 6

Explanation:

Step1: Analyze slope direction

The data points show a negative - slope trend as \(y\) decreases as \(x\) increases. So, we can eliminate equations with positive slopes (\(y=\frac{1}{4}x + 4\), \(y=\frac{1}{6}x+10\), \(y = \frac{1}{3}x+8\)).

Step2: Estimate \(y\) - intercept

The line of best - fit seems to cross the \(y\) - axis above \(y = 8\). For \(y=-3x + 9\), when \(x = 0\), \(y=9\); for \(y=-4x + 8\), when \(x = 0\), \(y = 8\); for \(y=-6x + 6\), when \(x = 0\), \(y=6\). The \(y\) - intercept of the line of best - fit should be close to 9.

Step3: Consider overall fit

By visually inspecting the data points and the remaining equations, \(y=-3x + 9\) seems to fit the data better than the other negative - slope equations.

Answer:

\(y=-3x + 9\)