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how do you Write Two-Variable Linear Equations

The cost, c, of a health club membership is related linearly to its length in months, m. If a 12-month membership costs $260 and an 18-month membership costs $380, which equation can be used to find the costof a 30-month membership?
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1 Answer

Cost C is linearly related to length in months M so:
 
C = S x M
 
Where S is the slope of the linear equation.
 
Now you need to find how C and M are related by using the other two membership costs to calculate the slope S of the linear equation. Think of them as two points on a graph at (12, 260) and (18, 380), from two points we can calculate the slope by calculating the quotient of the change in y (C) over the change in x (M):
 
S = (C2 - C1) / (M2 - M1)
   = (380 - 260) / (18 - 12)
   = (120) / (6) = 20
 
Now that we know the slope, we know the final equation as well:
 
C = 20 x M
 
Then you can simply plug in the 30 month answer into the M variable of the equation in order to find the cost for a 30 month membership.