To determine the correct slope that models Barton's car loan payments, we need to understand the situation. Barton's remaining balance decreases as he makes monthly payments. The slope (m) of a linear function is defined as the change in the y-value (amount in dollars) divided by the change in the x-value (months).
Barton took out a car loan of $2,625 and makes monthly payments of $175. Therefore, the slope represents the rate at which the remaining balance decreases.
Each month he pays $175, which can be represented as:
\[ \text{slope (m)} = \frac{\text{change in amount}}{\text{change in months}} = \frac{-175}{1} \]
Since we’re looking for the correct example from the options provided, let's substitute the values in each equation to find which one gives us a slope of -175. However, we may not need to compute all the values for this.
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m = (1,050 - 1,225) / (9 - 8): This would yield -175 in the numerator and 1 in the denominator, which equals -175 (but does not relate to Barton's payments).
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m = (2,450 - 2,625) / (0 - 1): This equals 175/-1 = -175 (potential fit).
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m = (525 - 700) / (11 - 12): This equals -175/-1 = 175 (not a fit).
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m = (9 - 8) / (1,050 - 1,225): This does not yield anything relevant to payments.
The second option would seem to correctly model the scenario, resulting in a slope that aligns with him losing $175 each month due to payments.
Thus, the correct answer modeling the correct slope is:
m = (2,450 - 2,625) / (0 - 1)
1 answer