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A student is given a table with pairs of x and y values. Some values are missing. The student needs to find the formula relating x and y, and then calculate the missing values m and n.

Mathematics

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Here are the solutions for the tables and problem-solving questions.

a)

  1. Determine the formula relating xx and yy.

    The difference in yy values is constant (11−10=111-10=1, 12−11=112-11=1). So, the slope is 1.
    Using (x,y)=(1,10)(x,y) = (1,10): 10=1(1)+c  ⟹  c=910 = 1(1) + c \implies c = 9.
    The formula is y=x+9y = x + 9.

  2. Fill in the missing values and calculate mm and nn.

    For x=5x=5 (the blank after 4): y=5+9=14y = 5+9 = 14.
    For $x=

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