Maths-
General
Easy

Question

In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the point (2, 2). If the point (20, w) lies on line k, what is the value of w?

The correct answer is: 74


    Hint:-
    Formula of a line in 2 Point form-
    y minus y subscript 1 equals open square brackets fraction numerator open parentheses y subscript 1 minus y subscript 1 close parentheses over denominator x subscript 2 minus x subscript 1 end fraction close square brackets cross times open parentheses x minus x subscript 1 close parentheses
    Step-by-step solution:-
    Since the points (0, -6) and (2, 2) lie on the given line k, we can find the equation of line k by using the 2 point formula-
    where x1 = 0, x1 = 2, y1 = -6, y2 = 2
    y minus y subscript 1 equals open square brackets fraction numerator open parentheses y subscript 1 minus y subscript 1 close parentheses over denominator x subscript 2 minus x subscript 1 end fraction close square brackets cross times open parentheses x minus x subscript 1 close parentheses
    y minus open parentheses negative 6 close parentheses equals open square brackets fraction numerator open curly brackets 2 minus open parentheses negative 6 close parentheses close curly brackets over denominator open parentheses 2 minus 0 close parentheses end fraction close square brackets cross times open parentheses x minus 0 close parentheses
    y plus 6 equals open square brackets fraction numerator open parentheses 2 plus 6 close parentheses over denominator 2 end fraction close square brackets cross times x
    ∴ y + 6 = open parentheses 8 over 2 close parentheses × x
    ∴ y + 6 = 4x
    ∴ y = 4x - 6 ------------------------ (Equation i)
    We are given that the point (20, w) lies on line k.
    ∴ substituting x = 20 & y = w in the equation of line k (From Equation i), we get-
    y = 4x - 6
    ∴ w = 4 (20) - 6
    ∴ w = 80 - 6
    ∴ w = 74
    Final Answer:-
    ∴ w = 74 is the value of w where point (20, w) lies on the given line k.

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