Question

select the correct answer.
a geologist gathered data about the total shoreline and maximum depth of several area lakes and organized the data into this table

total shoreline (miles)	22	17	10	23	12	35	7
maximum depth (feet)	101	85	59	113	64	158	33

she then used a graphing tool to display the data in a scatter plot, with x representing the total miles of shoreline and y representing the maximum depth. she also used the graphing tool to find the equation of the line of best fit:
y = 4.26x + 10.908.
based on the line of best fit, what is the approximate maximum depth of a lake that has 31 miles of shoreline?
a. 121 feet
b. 132 feet
c. 138 feet
d. 143 feet

Explanation:

Step1: Identify the formula and input

The line of best fit is \( y = 4.26x + 10.908 \), where \( x \) is the total shoreline (miles) and \( y \) is the maximum depth (feet). We need to find \( y \) when \( x = 31 \).

Step2: Substitute \( x = 31 \) into the formula

Substitute \( x = 31 \) into \( y = 4.26x + 10.908 \):
\( y = 4.26 \times 31 + 10.908 \)

Step3: Calculate the product

First, calculate \( 4.26 \times 31 \):
\( 4.26 \times 31 = 132.06 \)

Step4: Add the constant term

Then, add \( 10.908 \) to the result:
\( y = 132.06 + 10.908 = 142.968 \approx 143 \)

Answer:

D. 143 feet