A company buys a copy machine for $10,500 and is represented by the ordered pair (0,10,500). After 5 years, it is worth $5,500 and is represented by the ordered pair (5,5,500). What will the machine be worth in 10 years?
To find the equation of the line that represents the worth of the copy machine over time, we can use the formula for the equation of a line in slope-intercept form: y = mx + b. In this case, y represents the worth of the copy machine (in dollars) and x represents the number of years.
We are given two ordered pairs: (0,10,500) and (5,5,500). Plugging these values into the equation, we get two equations:
10,500 = m(0) + b
5,500 = m(5) + b
Since m(0) = 0, the first equation can be simplified to:
10,500 = b
Plugging this value into the second equation, we get:
5,500 = 5m + 10,500
Solving for m, we subtract 10,500 from both sides and divide by 5:
5,500 - 10,500 = 5m
-5,000 = 5m
m = -1,000
Now that we have the slope (m = -1,000) and the y-intercept (b = 10,500), we can write the equation for the worth of the copy machine over time:
y = -1,000x + 10,500
To find the worth of the machine in 10 years (x = 10), we plug it into the equation:
y = -1,000(10) + 10,500
y = -10,000 + 10,500
y = 5000
Therefore, the machine will be worth $5,000 in 10 years.