Mathematics
Grade-8
Easy

Question

Using the table of values, determine the equation of the line

  1. y = –3x – 9
  2. y = –3x + 3
  3. y = 3x – 9
  4. y = 3x + 3

Hint:

1. An equation refers to the relationship between 2 expressions represented with an equal to sign i.e. '='.
2. 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)

The correct answer is: y = 3x – 9


    GIVEN-
    (0,-9), (1,-6), (2,-3), (3,0) and (4,3) are the solutions of a line.
    TO FIND-
    Equation of the line.
    SOLUTION-
    We take any 2 points from the given table, say- (0,-9) and (1,-6) to find the equation of the given line using 2 point formual.
          (y-y1) = (y2-y1) * (x-x1)
                        (x2-x1)
    ∴ [y - (-9)] = [-6 - (-9)] * (x - 0)
                          (1 - 0)
    ∴    (y + 9) = (-6 + 9) * x
                           1
    ∴    (y + 9) = 3/1 * x
    ∴       y + 9 = 3x
    ∴             y = 3x - 9
    Final Answer:-
    Option 'c' i.e. 'y = 3x - 9' is the correct answer to the given question.

    Alternatively, we can substitute all the values of x & y in the equations given and check whether LHS = RHS or not.
    If all the points satisfy the given equation, that is the equation of the given line.
    However, since the given table has 5 solutions for the equation, this method would be more time consuming. Hence, we follow the 2 point formula method.
    However, final answer remains the same.

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