Mathematics
Grade-8
Easy

Question

John is trying to find the equation of the line(s) represented by the following graph.

  1. 4x – 5y = 10
  2. 4x + 5y = 10
  3. Y = 4x + 2
  4. Y = 4x - 2

Hint:

1. An equation refers to the relationship between 2 expressions represented with an equal to sign i.e. '='.
2. A point is said to be on a given line when the coordinates of that point when substituted in the given equation, satisfies the given equation.

The correct answer is: 4x – 5y = 10


    GIVEN-
    The given line passes through the points (0,-2) & (2.5,0) as shown in the given graph.
    TO FIND-
    Equation of the given line.
    SOLUTION-
    From the given graph, we observe that-
    (0,-2) & (2.5,0)
    We know that when a line passes through a given point, the coordinates of that point satisfies the equation of the said line.
    Hence, we substitute the coordiantes of both the point s in the given options to find the correct equation, for which LHS = RHS.
    a. 4x - 5y = 10
    We substitute (0,-2) in the given equation-
               4x - 5y = 10
    ∴ 4 (0) - 5 (-2) = 10
    ∴          0 + 10 = 10
    ∴                10 = 10
    ∴             LHS = RHS
    We substitute (2.5,0) in the given equation-
                 4x - 5y = 10
    ∴ 4 (2.5) - 5 (0) = 10
    ∴             10 - 0 = 10
    ∴                  10 = 10
    ∴               LHS = RHS
    Since both (0,-2) and (2.5,0) satisfy the given equation, 4x - 5y = 10 is the equation of the given line.
    Final Answer:-
    Option 'a' i.e. '4x - 5y = 10' is the correct answer to the given question.

    Alternatively, we can use the 2 point formula to find the equation of the given line-
    When we have 2 points that lie on a given line then we can find the equation of the said line by using the 2-point formula-
    (y-y1) = (y2-y1) * (x-x1)
                  (x2-x1)
    In the given question, x1 = 0, y1 = -2, x2 = 2.5 & y2 = 0
    ∴ (y-y1) = (y2-y1) * (x-x1)
                     (x2-x1)
    ∴ [y- (-2)] = [0 - (-2)] * (x - 0)
                         (2.5-0)
    ∴ (y + 2) =  2 *   x
                      2.5
    ∴ 2.5 * (y + 2) = 2x ................................... (Multiplying both sides by 2.5)
    ∴ 2.5y + 5 = 2x
    ∴ 5 = 2x - 2.5y
    ∴ 10 = 4x - 5y
    i.e. 4x - 5y = 10
    Final Answer remains the same.

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