Question

which equation could represent the line of best fit for this data? y = -3x + 28 y = -\frac{3}{2}x + 36 y = -3x + 36 y = -\frac{3}{2}x + 28 y = -\frac{3}{4}x + 28 y = -\frac{3}{4}x + 36

Explanation:

Step1: Determine the slope - general observation

As \(x\) increases, \(y\) decreases, so the slope is negative.

Step2: Estimate the slope value

Pick two approximate points, say \((2,36)\) and \((10,20)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{20 - 36}{10 - 2}=\frac{-16}{8}=- 2\). Looking at the options, the slopes of the lines are either \(-3\), \(-\frac{3}{2}\), or \(-\frac{3}{4}\). The slope of \(-\frac{3}{2}=-1.5\) is closer to our estimated slope compared to \(-3\) and \(-\frac{3}{4}\).

Step3: Estimate the y - intercept

The line seems to cross the \(y\) - axis around \(y = 36\).

Answer:

\(y=-\frac{3}{2}x + 36\)