Which linear equation represents the total value of the truck that depreciates approximately $4,200 per year and was bought for $42,935?
Understand the Problem
The question is asking which linear equation represents the total value of a truck that Alex bought, considering its depreciation over time. The total value of the truck can be represented with a linear equation where the initial value is $42,935 and it depreciates by $4,200 per year.
Answer
The correct equation is $y = -4,200x + 42,935$.
Answer for screen readers
The linear equation that represents the total value of the truck is:
$$ y = -4,200x + 42,935 $$
Steps to Solve
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Identify values Alex's truck has an initial value of $42,935 and depreciates by $4,200 each year. Here, the initial value represents the y-intercept (b) and depreciation the slope (m).
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Set up the linear equation The general form of a linear equation is given by:
$$ y = mx + b $$
where:
- ( y ) is the value of the truck after ( x ) years
- ( m ) is the slope (rate of depreciation, which is negative)
- ( b ) is the initial value
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Substituting values Here, ( m = -4,200 ) and ( b = 42,935 ).
So the equation becomes:
$$ y = -4,200x + 42,935 $$ -
Compare with the options Now, we can find the correct match for the linear equation among the provided options.
The linear equation that represents the total value of the truck is:
$$ y = -4,200x + 42,935 $$
More Information
This equation shows that for each year (x), the value of the truck decreases by $4,200 from the initial price of $42,935.
Tips
- Not using a negative sign for depreciation: Ensure to remember that depreciation reduces the value of an asset, thus it should be negative.
- Misplacing the initial value: The initial value should always be added, not multiplied or placed incorrectly.
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