Answered

Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Get prompt and accurate answers to your questions from our community of knowledgeable experts.

6. Make Sense and Persevere If x represents the number of
years
since 2000 and y represents the gas price, predict what
the difference between the gas prices in 2013 and 2001 is?
Round to the nearest hundredth.

Sagot :

MrRoyalidn

The difference between the gas prices in 2013 and 2001 is 3.00

Graphing tool

See attachment for the graph of the line of best fit

The equation

Start by calculating the slope of the line of best fit using:

[tex]b = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

From the line of best fit, we have:

[tex]b = \frac{3 -2}{8 -4}[/tex]

The regression equation is then represented as:

[tex]\^y = b(\^x - x_1) + y_1[/tex]

So, we have:

[tex]\^y = \frac 14 (\^x - 4) + 2[/tex]

[tex]\^y = \frac 14\^x - 1 + 2[/tex]

[tex]\^y = \frac 14\^x + 1[/tex]

So, the linear regression equation is:

[tex]\^y = \frac 14\^x + 1[/tex]

In 2001, the value of x is 1.

So, we have:

[tex]\^y_1 = \frac 14\times (1) + 1[/tex]

[tex]\^y_1 = 1.25 \\[/tex]

In 2013, the value of x is 13.

So, we have:

[tex]\^y_2 = \frac 14\times (13) + 1[/tex]

[tex]\^y_2 = 4.25[/tex]

So, the difference (d) between the prices is:

[tex]d = 4.25 - 1.25[/tex]

[tex]d = 3.00[/tex]

Hence, the difference between the gas prices in 2013 and 2001 is 3.00

Read more about linear regression at:

https://brainly.com/question/17844286

View image MrRoyal
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.