Depreciation A small business buys a computer for 4000 . After 4 years the value o

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Depreciation A small business buys a computer for ...

$$ \begin{array}{l}{\text { Depreciation A small business buys a computer for }} \\ {\$ 4000 \text { . After } 4 \text { years the value of the computer is expected }} \\ {\text { to be } \$ 200 . \text { For accounting purposes the business uses lin- }} \\ {\text { ear depreciation to assess the value of the computer at a }} \\ {\text { given time. This means that if } V \text { is the value of the com- }} \\ {\text { puter at time } t \text { , then a linear equation is used to relate } V} \\ {\text { and } t .}\end{array} $$ $$ \begin{array}{l}{\text { (a) Find a linear equation that relates } V \text { and } t} \\ {\text { (b) Sketch a graph of this linear equation. }} \\ {\text { (c) What do the slope and } V \text { -intercept of the graph }} \\ {\text { represent? }} \\ {\text { (d) Find the depreciated value of the computer } 3 \text { years from }} \\ {\text { the date of purchase. }}\end{array} $$

$$
\begin{array}{l}{\text { Depreciation A small business buys a computer for }} \\ {\$ 4000 \text { . After } 4 \text { years the value of the computer is expected }} \\ {\text { to be } \$ 200 . \text { For accounting purposes the business uses lin- }} \\ {\text { ear depreciation to assess the value of the computer at a }} \\ {\text { given time. This means that if } V \text { is the value of the com- }} \\ {\text { puter at time } t \text { , then a linear equation is used to relate } V} \\ {\text { and } t .}\end{array}
$$
$$
\begin{array}{l}{\text { (a) Find a linear equation that relates } V \text { and } t} \\ {\text { (b) Sketch a graph of this linear equation. }} \\ {\text { (c) What do the slope and } V \text { -intercept of the graph }} \\ {\text { represent? }} \\ {\text { (d) Find the depreciated value of the computer } 3 \text { years from }} \\ {\text { the date of purchase. }}\end{array}
$$

Key Concepts

Slope and Intercept

In a linear equation, the slope is the constant rate of change, which in depreciation represents the annual loss in value. The y-intercept (or V?intercept in this context) is the value of the asset at the start, typically its purchase price. These components help in understanding both the initial cost and the rate at which the asset loses value.

Depreciation

Depreciation refers to the method of allocating the cost of an asset over its useful life. It represents how an asset loses value over time due to factors such as usage, wear and tear, or obsolescence. This concept is crucial for accounting and financial analysis because it helps businesses spread the cost of assets and match expenses with the revenue they help generate.

Linear Depreciation

Linear depreciation is a specific method where the asset’s loss in value is distributed evenly across each time period, resulting in a constant amount of depreciation each period. This approach simplifies accounting and forecasting by assuming that the asset depreciates at a steady rate over its useful life.

Linear Equations

A linear equation represents a straight-line relationship between two variables. In the context of depreciation, it is used to model how the value of an asset decreases over time. The general form, V = mt + b, allows us to calculate the asset’s value at any given time by establishing a constant rate of change and a starting value.

Graphing Linear Functions

Graphing linear functions involves plotting the relationship between the two variables as a straight line. This visual representation helps in understanding the trend over time, where the x-axis typically represents time and the y-axis represents the value of the asset. It is a useful tool in analyzing and predicting future values based on the constant rate of depreciation.

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