Question

which equation could represent the line of best fit for this data? y = \frac{1}{4}x + 6 y = -\frac{1}{2}x + 16 y = \frac{1}{3}x + 8 y = x y = -6x + 18 y = -3x + 12

Explanation:

Step1: Observe the data trend

The data points seem to have a negative - slope trend overall, so we can rule out equations with positive slopes like $y=\frac{1}{4}x + 6$, $y=\frac{1}{3}x+8$ and $y = x$.

Step2: Estimate the slope and y - intercept

We can roughly estimate the slope by looking at the change in $y$ over the change in $x$. Also, we can estimate the $y$-intercept (the value of $y$ when $x = 0$). The $y$-intercept seems to be around 16. Among the remaining options with negative slopes ($y=-\frac{1}{2}x + 16$, $y=-6x + 18$, $y=-3x + 12$), the slope of $y =-\frac{1}{2}x+16$ seems to match the gentle negative - slope of the data points better. The slopes of $y=-6x + 18$ and $y=-3x + 12$ are too steep compared to the data trend.

Answer:

$y =-\frac{1}{2}x + 16$