Maths-
General
Easy

Question


The table shows several values of x and their corresponding values of f(x). The function f is defined by f(x) = mx + b, where  and  are constants. What is the value of b ?
 

The correct answer is: 16


    HINT: Find slope and then find value of b using point-slope form.
    Complete step by step Solution
    From the table,
    we have 2 points open parentheses x subscript 1 comma y subscript 1 close parentheses equals left parenthesis 2 comma 106 right parenthesis and open parentheses x subscript 2 comma y subscript 2 close parentheses equals left parenthesis 3 comma 151 right parenthesis.
    We can find slope m equals fraction numerator open parentheses y subscript 2 minus y subscript 1 close parentheses over denominator open parentheses x subscript 2 minus x subscript 1 close parentheses end fraction equals fraction numerator 151 minus 106 over denominator 3 minus 2 end fraction equals 45.
    Hence, m = 45.
    We know that point-slope form is y minus y subscript 1 equals m open parentheses x minus x subscript 1 close parentheses
    By substituting the values,
    we get y - 106 = 45(x - 2).
    On adding 106 on both the sides,
    we get y = 45x + 16 which is of the form y = mx + b.
    Hence, the value of b is 16.
     

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