Question
Match the equation that represents the relationship.
- a = b/5
- a = b*5
- b = a*5
- b = a + 8
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: a = b/5
GIVEN-
x1 = 2, y1 = 10, x2 = 5, y2 = 25, x3 = 7, y3 = 35, x4 = 10, y4 = 50, x5 = 12, y5 = 60
TO FIND-
Equation that matches the given coordinates
SOLUTION-
we observe that (2,10) and (5,25) 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-10)/ (x-2) = (25-10)/ (5-2)
∴ (y-10)/ (x-2) = 15/3
∴ (y-10)/ (x-2) = 5/1 ............................. (Dividing numerator and denominator by 3)
∴ 1 (y-10) = 5 (x-2) ...................... (Cross multiplying)
∴ y - 10 = 5x - 10
∴ y = 5x - 10 + 10 ....................... (Adding both sides with 10)
∴ y = 5x
In the given sum, x coordinates are represented by a and y coordinates by b
∴ b = 5a
FINAL ANSWER-
Option 'c' i.e. 'b = a * 5' is the correct answer to the given question.
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