Question

8 multiple choice 1 point selena graphed the data she collected in her chemistry class and needs to find the line of best fit. if the data and line are shown on the graph, what is the equation of her line of best fit? y = -\frac{1}{3}x + 1 y = \frac{1}{3}x y = -\frac{1}{3}x y = -3x + 1

Explanation:

Step1: Determine the slope

The line of best - fit passes through the origin \((0,0)\) and another point, say \((3,1)\). The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 0,y_1=0,x_2 = 3,y_2 = 1\), so \(m=\frac{1 - 0}{3 - 0}=\frac{1}{3}\).

Step2: Determine the y - intercept

Since the line passes through the origin \((0,0)\), the y - intercept \(b = 0\). The equation of a line in slope - intercept form is \(y=mx + b\). Substituting \(m=\frac{1}{3}\) and \(b = 0\) gives \(y=\frac{1}{3}x\).

Answer:

\(y=\frac{1}{3}x\) (the second option)