Question

charged. write an equation of a line of fit for the data. round all values to the nearest tenth.

ticket price (dollars), x	17	20	22	26
tickets sold, y	450	423	400	395

$y=square x+square$

Explanation:

Step1: Calculate means

Let $x_1 = 17,x_2=20,x_3 = 22,x_4=26$ and $y_1 = 450,y_2=423,y_3 = 400,y_4=395$.
The mean of $x$ values, $\bar{x}=\frac{17 + 20+22+26}{4}=\frac{85}{4}=21.25$.
The mean of $y$ values, $\bar{y}=\frac{450 + 423+400+395}{4}=\frac{1668}{4}=417$.

Step2: Calculate numerator and denominator for slope

The numerator for the slope $m$:
\[

$$\begin{align*} \sum_{i = 1}^{4}(x_i-\bar{x})(y_i - \bar{y})&=(17 - 21.25)(450-417)+(20 - 21.25)(423 - 417)+(22-21.25)(400 - 417)+(26-21.25)(395 - 417)\\ &=(- 4.25)\times33+(-1.25)\times6 + 0.75\times(-17)+4.75\times(-22)\\ &=-140.25-7.5-12.75 - 104.5\\ &=-265 \end{align*}$$

\]
The denominator for the slope $m$:
\[

$$\begin{align*} \sum_{i = 1}^{4}(x_i-\bar{x})^2&=(17 - 21.25)^2+(20 - 21.25)^2+(22-21.25)^2+(26-21.25)^2\\ &=(-4.25)^2+(-1.25)^2+(0.75)^2+(4.75)^2\\ &=18.0625 + 1.5625+0.5625+22.5625\\ &=42.75 \end{align*}$$

\]
The slope $m=\frac{-265}{42.75}\approx - 6.2$.

Step3: Calculate y - intercept

We know that the equation of a line is $y=mx + b$. Using the point $(\bar{x},\bar{y})=(21.25,417)$ and $m=-6.2$.
$417=-6.2\times21.25 + b$.
$417=-131.75 + b$.
$b=417 + 131.75=548.75\approx548.8$.

Answer:

$y=-6.2x + 548.8$