What are the equations for these paterns?

1 lap $1 $2

2 laps $3 $3.50

3 laps $5 $5

4 laps $7 $6.50

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We set up the following linear equations, in accordance with the quantities and try determine x,y .

x+y=2

2x+3y=3.5

3x+5y=5

4x+7y=6.5

From (1) and (4) eliminating x we get,

(4)-3*(1): 3y=6.5-8=-1.5. Therefore, **y**= -1.5/3= **-0.5**. Re substituting this value of y in(1), x-0.5 =2=>**x =2.5**.

We see that the value of x and y fits well to all the patterns.

We see that the numbers corresponding to 1 lap are $1 and $2, for an increase in the number of laps by 1, the first number increases by 2 and the next by 1.5. Let the number of laps be x which is the independent variable, and the number in the 2nd and 3rd columns be represented by y1 and y2.

We get the equations:

y1 = 1 + 2(x - 1) and y2 = 2 + 1.5(x - 1).

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