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.
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?
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