Question

which equation could represent the line of best fit for this data? y = -\frac{4}{3}x + 30 y = -\frac{1}{3}x + 32 y = -\frac{2}{3}x + 36 y = -x + 28 y = -3x + 40 y = -2x + 38

Explanation:

Step1: Analyze slope visually

The data points show a negative - sloping trend. We can estimate the slope by looking at the general direction of the points. As \(x\) increases, \(y\) decreases.

Step2: Estimate \(y\) - intercept

The \(y\) - intercept is the value of \(y\) when \(x = 0\). By looking at the spread of the points, we can estimate where the line would cross the \(y\) - axis.

Step3: Check equations

We know the slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
For \(y =-\frac{4}{3}x + 30\), slope \(m=-\frac{4}{3}\approx - 1.33\).
For \(y =-\frac{1}{3}x + 32\), slope \(m =-\frac{1}{3}\approx - 0.33\).
For \(y=-\frac{2}{3}x + 36\), slope \(m=-\frac{2}{3}\approx - 0.67\).
For \(y=-x + 28\), slope \(m=-1\).
For \(y=-3x + 40\), slope \(m=-3\).
For \(y=-2x + 38\), slope \(m=-2\).
Visually, the slope seems to be around \(-\frac{2}{3}\) and the \(y\) - intercept seems to be around 36.

Answer:

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