Question

the average price of an acre of land in some country was $1126 in 2001. in 2006, the price rose to approximately $1581

a. write two ordered pairs of the form (year, price of acre).

b. find the slope of the line through the two points.

c. write a sentence explaining the meaning of the slope as a rate of change.

a. two ordered pairs of the form (year, price of acre) are (2001, 1126),(2006, 1581).

(use a comma to separate answers as needed.)

b. the slope of the line through the two points is approximately 91.

c. choose the correct interpretation of the slope.

a. the price per acre increased at a rate of about $91 per year.

b. time increased at a rate of about 91 years per dollar of price per acre.

c. the price per acre increased at a rate of $91 per 91 years.

d. the price increased at a rate of about $1 per 91 years.

Explanation:

Step1: Find two ordered pairs

Given ordered pairs: \((2001,1126)\) and \((2006,1581)\)

Step2: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Here, \(x_1 = 2001,y_1=1126,x_2 = 2006,y_2 = 1581\)
\(m=\frac{1581 - 1126}{2006 - 2001}=\frac{455}{5}=91\)

Step3: Interpret the slope

The slope \(m = 91\) means that the price of land per - acre increased at a rate of about \(\$91\) per year.

Answer:

a. \((2001,1126),(2006,1581)\)
b. The slope of the line through the two points is \(m = 91\)
c. The price of land per - acre increased at a rate of about \(\$91\) per year. So the answer is A.