Maths-
General
Easy

Question

For the linear function f, f(2) = 10 and the graph of y = f(x) in the xy - plane has a slope of 3 . Which equation defines f ?

  1. f left parenthesis x right parenthesis equals 2 x plus 12    
  2. f left parenthesis x right parenthesis equals 2 x plus 8    
  3. f left parenthesis x right parenthesis equals 3 x plus 10    
  4. f left parenthesis x right parenthesis equals 3 x plus 4    

The correct answer is: f left parenthesis x right parenthesis equals 3 x plus 4


    HINT: Use point-slope form and get the equation.
    Complete step by step Solution
    Given f left parenthesis 2 right parenthesis equals 10,
    So, we get a point left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis with x subscript 1 end subscript equals 2 andblank y subscript 1 end subscript equals 10
    That is, left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis equals left parenthesis 210 right parenthesis
    Slope m equals 3 (given)
    When we are given a slope and a point, we can use point-slope form to get the equation of the line.
    We know that point-slope form is y minus y subscript 1 end subscript equals m left parenthesis x minus x subscript 1 end subscript right parenthesis.
    On substituting the point and the slope in the equation,
    We get y minus 10 equals 3 left parenthesis x minus 2 right parenthesis.
    On simplification, we get y equals 3 x plus 4.
    Therefore y equals 3 x plus 4 defines the f.
    Hence option D is the answer.

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