SOLUTION: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $350 for 420 mi and in June her cost was $470 for 900 mi. Assum

Algebra ->  Linear-equations -> SOLUTION: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $350 for 420 mi and in June her cost was $470 for 900 mi. Assum      Log On


   

Question 644067: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $350 for 420 mi and in June her cost was $470 for 900 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance driven d.
(a) Find a linear equation that relates C and d.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The general form of the equation is
+C+=+m%2Ad+%2B+b+ where +m+ is the slope
Plot +C+ on the vertical axis
Plot +d+ on the horizontal
Slope is ( change in C ) / ( change in d )
+%28+470+-+350+%29+%2F+%28+900+-+420+%29+
+120+%2F+480+=+1%2F4+
------------------
+m+=+1%2F4+
Now just plug in one of the 2 given points
to find +b+, the intercept on the vertical axis
+470+=+%281%2F4%29%2A900+%2B+b+
+b+=+470+-+225+
+b+=+245+
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The equation is +C+=+%281%2F4%29%2Ad+%2B+245+
check answer:
+350+=+%281%2F4%29%2A420+%2B+245+
+350+=+105+%2B+245+
+350+=+350+
Here's the plot:
+graph%28+400%2C+400%2C+-100%2C+1000%2C+-100%2C+500%2C+%281%2F4%29%2Ax+%2B+245+%29+