explain how to draw a line of best fit through a set of data points in a scatterplot. then, use the points…

Explanation:

Step 1: Draw the Line of Best Fit

To draw the line of best fit, we visually estimate a line that passes as close as possible to the majority of the data points in the scatter plot. The goal is to balance the number of points above and below the line.

Step 2: Identify Two Points on the Line

We are given two points ((-4, -2)) and ((1, -4)) that lie on or near the line of best fit. We can use these two points to find the equation of the line.

Step 3: Calculate the Slope ((m))

The slope (m) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by the formula: [ m = \frac{y_2 - y_1}{x_2 - x_1} ] Substituting (x_1 = -4), (y_1 = -2), (x_2 = 1), and (y_2 = -4): [ m = \frac{-4 - (-2)}{1 - (-4)} = \frac{-4 + 2}{1 + 4} = \frac{-2}{5} = -\frac{2}{5} ]

Step 4: Use the Point-Slope Form to Find the Equation

The point-slope form of a line is (y - y_1 = m(x - x_1)). We can use one of the points, say ((-4, -2)), and the slope (m = -\frac{2}{5}): [ y - (-2) = -\frac{2}{5}(x - (-4)) ] Simplify: [ y + 2 = -\frac{2}{5}(x + 4) ]

Step 5: Convert to Slope-Intercept Form ((y = mx + b))

Expand the right-hand side: [ y + 2 = -\frac{2}{5}x - \frac{8}{5} ] Subtract 2 from both sides. Remember that (2 = \frac{10}{5}): [ y = -\frac{2}{5}x - \frac{8}{5} - \frac{10}{5} ] [ y = -\frac{2}{5}x - \frac{18}{5} ]

Answer:

The equation of the line of best fit in slope-intercept form is (y = -\frac{2}{5}x - \frac{18}{5}).