Question

using the desmos calculator, find the line of best fit. round to the nearest tenth.

x	y
-8	7
-5	3
3	6
9	0

$y = 0.27x + 3.94$
$y = 1.25x + 3.75$
$y = 3.93x + -0.27$
$y = -0.27x + 3.93$

Explanation:

Step1: List data points

Data points: $(-8,7), (-5,3), (3,6), (9,0)$

Step2: Calculate slope ($m$)

First, find means:
$\bar{x} = \frac{-8 + (-5) + 3 + 9}{4} = \frac{-1}{4} = -0.25$
$\bar{y} = \frac{7 + 3 + 6 + 0}{4} = \frac{16}{4} = 4$
Calculate numerator for $m$:
$\sum (x_i - \bar{x})(y_i - \bar{y}) = (-8+0.25)(7-4) + (-5+0.25)(3-4) + (3+0.25)(6-4) + (9+0.25)(0-4)$
$= (-7.75)(3) + (-4.75)(-1) + (3.25)(2) + (9.25)(-4)$
$= -23.25 + 4.75 + 6.5 - 37 = -49$
Calculate denominator for $m$:
$\sum (x_i - \bar{x})^2 = (-8+0.25)^2 + (-5+0.25)^2 + (3+0.25)^2 + (9+0.25)^2$
$= 60.0625 + 22.5625 + 10.5625 + 85.5625 = 178.75$
$m = \frac{-49}{178.75} \approx -0.27$

Step3: Calculate intercept ($b$)

$b = \bar{y} - m\bar{x} = 4 - (-0.27)(-0.25) = 4 - 0.0675 \approx 3.93$

Step4: Form line equation

$y = mx + b$

Answer:

$y = -0.27x + 3.93$