Amber H.

asked • 07/18/16

Analytical Geometry

The cost C (in dollars) of a taxi ride consists of a starting amount plus an amount which depends on the distance D (in kilometres) you take the taxi. The equation is C=0.35D+3.50. This is a linear equation with the variables C and D.
 
A)Which is the independent variable, and why? 
B)Calculate the C and D-intercepts.
C)What, if any, meaning can you give to the C and D-intercepts? 

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Mark M. answered • 07/18/16

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A) the distance, because it determines the cost
B) (0, 3.50) and (3.50, 0)
C) If you travel zero km you still pay $3.50 and if you pay $3.50 you have traveled zero miles
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Michael W.

If we drew the graph, we'd put the distance along the x-axis--the independent variable, as you said--and then we'd put the cost on the y-axis.
 
So, the "Cost" intercept (y-intercept) is where the Distance is equal to 0.  So, we plug in 0 for D, and we calculate C, which ends up being $3.50.  I'm with you so far...
 
...but to calculate the "Distance" intercept, you have to plug in 0 for the cost in the equation, and figure out what value of D would get us a cost of 0. 
 
0 = 0.35D + 3.50
 
And then solve for D.  You don't get 3.5...  In fact, I think you get a negative distance!  So part of the challenge in this problem is to interpret what that means, but hopefully, at least this gets the student on the right track.
 
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07/18/16

Mark M.

Absolutely true. If the cost is $0, (actually impossible because of the starting amount), then one would have driven -10 miles. (Is time travel allowed?).
This is an opportunity to emphasis the validity of an algebraic solution versus the validity of a real life solution.
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07/18/16

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