Question

a cafeteria worker is wondering how student lunch prices at a high school have changed over time. she researches lunch prices for the years 2000 through 2015 and plots the data in a scatter plot. the best-fit line for the data has the equation y=0.057 x + 1.150, where x is the number of years since 2000 and y is the student lunch price, in dollars.
determine whether each statement below is true ot false based on the question of the line best fit. select true or false for each question.

the student lunch price was generally increasing between 2000 and 2015.

the student lunch price was changed by approximately 5.7 cents a year.

the student price in 2015 was approximately $1.15.

Answer 1

Answer:

True false true

Step-by-step explanation:

Answer 2

TRUE, the student lunch price was generally increasing between 2000 and 2015 as the equation $y=0.057x+1.150$  is a linearly increasing function.

TRUE, the student lunch price was changed by approximately $5.7\rm cents$  a year.

FALSE, the student price in 2015 was approximately $1.15.

The best-fit line for the data has the equation  $y=0.057x+1.150$ , where $x$ is the number of years since 2000 and $y$  is the student lunch price, in dollars.

So, it can be seen here from the best-fit line equation that it is a linearly increasing function so, the student lunch price was generally increasing between 2000 and 2015.

Now, differentiating the given best-fit line for the data has the equation  $y=0.057x+1.150$ with respect to $x$ to determine the approximated change of the lunch price per year

$\dfrac{dy}{dx}=\dfrac{d}{dx}(0.057x+1.150)\\\dfrac{dy}{dx}=\ 0.057\\\dfrac{dy}{dx}=5.7\rm cents$

And, $2015$ is $15$ years from the year $2000$ so, substitute the value of the parameter $x=15$ in the best-fit line equation, we get

$y=0.057\times 15 +1.150\\y=0.855+1.150\\y=2.005$

So, the lunch price in 2015 was approximately $\ 2.005$.

Hence, the first two statements are TRUE while the last statement is FALSE.

Learn more about the best-fit line equation here:

https://brainly.com/question/14279419?referrer=searchResults