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The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $380 for 480 mi and in June her cost was $450 for 830 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance x driven. Find a linear equation that relates C and d.

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opudodennis

Answer:

[tex]y=0.2x+284[/tex]

Step-by-step explanation:

Let  x be the distance driven, d-distance and C our constant.

Our information can be presented as:

[tex]y=mx+c\\\\450=830x+C\ \ \ \ \ \ \ \ \ eqtn 1\\\\380=480x+C\ \ \ \ \ \ \ \ \ eqtn 2[/tex]

#Subtracting equation 2 from 1:

[tex]70=350x\\x=0.2[/tex]

Hence the fixed cost per mile driven,[tex]x[/tex] is $0.20

To find the constant,[tex]C[/tex] we substitute [tex]x[/tex] in any of the equations:

[tex]450=830x+C\ \ \ \ \ \ \ X=0.2\\\therefore C=450-830\times0.2\\=284[/tex]

Now, substituting our values in the linear equation:

[tex]y=0.2x+284[/tex]       #y=cost of driving, x=distance driven

Hence the linear equation for the cost of driving is y+0.2x+284

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