Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

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.