how do you Write Two-Variable Linear Equations

Question

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?

Answer 1

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.