Question

math of finance sem a- a
bobile ownership
depreciation of computer system
what is the slope of the line?
the graph shows the straight-line depreciation of a computer system
initially valued at $5,000 across a span of 3 years. round to the nearest
dollar.
depreciation of computer system
6,000
у
5,000
computer system value
4,000
3,000
2,000
1,000
x
1 2 3 4
years

Explanation:

Step1: Identify two points on the line

From the graph, we can see that when \( x = 0 \) (initial time, 0 years), \( y = 5000 \) (initial value of the computer system). When \( x = 3 \) (after 3 years), \( y = 0 \) (the value of the computer system is 0 at the end of 3 years). So the two points are \((0, 5000)\) and \((3, 0)\).

Step2: Use the slope formula

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line. Let \((x_1,y_1)=(0, 5000)\) and \((x_2,y_2)=(3, 0)\).

Substitute the values into the formula:
\( m=\frac{0 - 5000}{3 - 0}=\frac{- 5000}{3}\approx - 1667\) (rounded to the nearest dollar)

Answer:

-1667 (rounded to the nearest dollar)