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Question

Jin is tracking how much food he feeds his dogs each week . After 2 weeks , he has used 8.5 cups of dog food. After 5 weeks , he has used 21.25 cups. Construct a function in the form y = mx + b to represent the amount of dog food used , y , after x weeks .

hintHint:

Use two – point form

The correct answer is: y = 8.5x


     It is given that no of weeks = x
    Amount of dog food used = y cups
    Acc. To question, x1 = 2 and y1 = 8.5
    x2 = 5 and y2 = 21.25
    Using two – point form, equation of the line is
    (y – y1) = m (x – x1)  where  m = fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction

    rightwards double arrow m = fraction numerator 21.25 minus 8.5 over denominator 5 minus 2 end fraction

         = fraction numerator 12.75 over denominator 3 end fraction =  4.25
    Now,  equation of the line is (y – y1) = m (x – x1)
    (y – 8.5) = 4.25 (x – 2)
    y – 8.5 = 4.25x – 8.5
    y = 8.5x + 0
    y = 8.5x
    A linear function that represents the relationship between amount of dog food used after certain weeks is y = 8.5x .

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