Question

identifying straight-line depreciation equation from a graph
the graph shows the depreciation for a truck.
which equation represents the straight - line depreciation for the truck?
truck depreciation
options:
$d(t)=50,000t + 2,500$
$d(t)= - 50,000t + 2,500$
$d(t)=2,500t - 50,000$
$d(t)= - 2,500t + 50,000$ (assuming the last option is mis - ocred and should be like this for a reasonable depreciation problem)

Explanation:

Step1: Identify initial value (y-intercept)

The graph starts at $t=0$ with value $\$50,000$, so $b=50000$.

Step2: Calculate slope (depreciation rate)

Slope $m=\frac{\text{Final Value}-\text{Initial Value}}{\text{Time Elapsed}}=\frac{0-50000}{20-0}=-2500$.

Step3: Form linear equation

Use $D(t)=mt+b$, substitute $m=-2500$, $b=50000$.
$D(t)=-2500t+50000$

Answer:

$D(t) = -2,500t + 50,000$ (the fourth option, matching the derived equation)