I am having ahard time solving this problem and am not good with story problems, could someone please help. Can you show how you would write out problem.
The average price of an acre of U.S farmland was $1132 in 2001. In 2006, the price of an arce rose to approximately $1657.
a. Write two order pairs of the form (year, price of acre)
b. find the slope of the line through the two points
Explain the meaning of the slope as a rate change.
In 2001, aver. price of an acre = $1132
In 2006, aver. price of an acre = $1657
a. 2001 = 0, 1132; 2006 = 5, 1657
2001 would be the starting year and 2006 would be 5 years later
The ordered pairs would be,
(0,1132), (5,1657)
b. slope
m = y2 - y1/(x2 - x1)
m = 1657 - 1132/(5 - 0)
m = 525/5
m = 105
The equation of the line with
slope m = 105, and point (5,1657)
y = mx + b
y = 105x + b
1657 = 105(5) + b
1657 = 525 + b
b = 1132
Therefore, the equation is
y = 105x + 1132
Explain the meaning of the slope as a rate change.
See this website for an excellent explanation.
http://www.purplemath.com/modules/slopyint.htm
a. To write two ordered pairs of the form (year, price of acre), we need to identify the years when the prices were recorded and the corresponding prices.
Let's say the year 2001 corresponds to the price $1132 and the year 2006 corresponds to the price $1657. We can write the ordered pairs as follows:
(2001, $1132)
(2006, $1657)
b. To find the slope of the line through the two points, we can use the slope formula, which is:
slope = (change in y) / (change in x)
In this case, the change in y is the difference in prices ($1657 - $1132), and the change in x is the difference in years (2006 - 2001).
So, the slope can be calculated as:
slope = ($1657 - $1132) / (2006 - 2001)
Now, let's compute the values:
slope = $525 / 5
Simplifying this equation, we find that:
slope = $105
c. The meaning of the slope as a rate of change in this context is that, on average, the price of an acre of U.S farmland increased by $105 per year between 2001 and 2006. This indicates the rate at which the price of an acre of farmland was rising over that five-year period.