To determine the equation of theline of best fit, we will be needing a few things. First, we need to calculate the average (mean) of the x-values.
To find the mean, we simply add all of the x-values, then divide it by the number of addends.
The mean x-value is 6, calculated as follows:
[tex]\frac{2+4+6+8+10}{5}=6[/tex]
Then, we also do the same for the y-values; wee look for the mean.
[tex]\frac{1146+1556+1976+2395+2490}{5}=1912.6[/tex]
The mean y-value is 1,912.6.
We will use theses means t osolve for the slope m using the equation:
[tex]m=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}[/tex][tex]\begin{gathered} m=\frac{(2-6)(1146-1912.6)+(4-6)(1556-1912.6)+(6-6)(1976-1912.6)+(8-6)(2395-1912.6)+(10-6)(2490-1912.6)}{(2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2} \\ \\ m=176.35 \end{gathered}[/tex]
So m = 176.35.
Finally, we solve for b using the equation:
[tex]b=\bar{y}-m\bar{x}[/tex][tex]\begin{gathered} b=1912.6-176.35(6) \\ b=854.5 \end{gathered}[/tex]
So b = 854.5.
Now we can write the full equation of the best-fit line:
y = 176.35x + 854.5
If the resort reports 15 inches of new snow, then we use x = 15 to solve for y using the equation of the best-fit line to approximate the number of snowsliders.
[tex]\begin{gathered} y=176.35x+854.5 \\ y=176.35(15)+854.5 \\ y=3499.75 \end{gathered}[/tex]
We round off this value to 3,500 since we are looking for number of people.
The answer is 3,500.
