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Does the following scenario represent a direct variation?

Green Cab Company charges a flat fee of $5.50 and an additional $1.20 per minute.

1. Yes
2. No

User Floorish
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1 Answer

3 votes

Final answer:

2) No, the Green Cab Company's pricing does not represent a direct variation since there is a flat fee in addition to a per-minute charge. Direct variation would only involve a rate multiplied by the variable quantity without any added constant or flat fee.

Step-by-step explanation:

The scenario described for Green Cab Company does not represent a direct variation because a direct variation implies that there is a direct proportion between two variables, without any additional charges or fees. In direct variation, the equation would take the form of y = kx, where k is the constant of variation and there is no y-intercept other than zero. However, because Green Cab Company charges a flat fee of $5.50 in addition to $1.20 per minute, the existence of this flat fee means that the relationship is linear, but not a direct variation. A similar concept is found when looking at the linear equation for the auto mechanic's labour costs, which is expressed as y = 75 + 55x, demonstrating a flat fee plus a variable rate per hour. The slope and y-intercept of this equation are $55 and $75, respectively, signifying a fixed charge and an hourly rate. This also is a linear relationship, not a direct variation due to the fixed fee.

User FireFoxII
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