Mathematics
Grade6
Easy
Question
The table below shows the relationship between x and y. Choose the equation that represents the same relationship.
- y = 4x
- y = x - 9
- y = 1/4 x
- y = x + 9
Hint:
An equation represents the relationship between 2 coordinates viz. x & y.
To find the equation that matches the coordinates given in the table, we use 2 point formula of a line i.e.-
(y-y1)/ (x-x1) = (y2-y1)/ (x2-x1)
The correct answer is: y = 1/4 x
GIVEN-
x1 = 12, y1 = 3, x2 = 20, y2 = 5, x3 = 28, y3 = 7, x4 = 36, y4 = 9
TO FIND-
Equation that matches the given coordinates
SOLUTION-
we observe that (12,3) and (20,5) are 2 points on the given line.
Hence, we use 2 point formula of a line to find its equation.
(y-y1)/ (x-x1) = (y2-y1)/ (x2-x1)
∴ (y-3)/ (x-12) = (5-3)/ (20-12)
∴ (y-3)/ (x-12) = 2/8
∴ (y-3)/ (x-12) = 1/4 ............................. (Dividing numerator & denominator by 2)
∴ 4 (y-3) = 1 (x-12) ...................... (Cross multiplying)
∴ 4y - 12 = x - 12
∴ 4y = x - 12 + 12 ....................... (Adding both sides with 12)
∴ 4y = x
∴ y = 1/4 * x ............................... (Dividing both sides by 4)
FINAL ANSWER-
Option 'c' i.e. 'y = 1/4x' is the correct answer to the given question.
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