Mathematics
Grade-8
Easy
Question
Using the table of values, determine the equation of the line
- y = –3x – 9
- y = –3x + 3
- y = 3x – 9
- 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.
