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: Observe data trend

The data points seem to have a positive - slope trend. So, we can rule out equations with negative slopes ($y=-3x + 9$ and $y=-6x + 6$).

Step2: Estimate y - intercept

The data points seem to cross the y - axis around $y = 4$. The equation $y=\frac{1}{4}x+4$ has a y - intercept of 4 and a reasonable positive slope compared to the data distribution. The equation $y=\frac{1}{6}x + 10$ has a y - intercept of 10 which is too high, and $y = 4x+8$ has a very steep slope compared to the data, and $y=\frac{1}{3}x + 8$ has a y - intercept of 8 which is also high.

Answer:

$y=\frac{1}{4}x + 4$