Mathematics
Grade6
Easy
Question
Find the algebraic equation that shows the relationship between the independent and dependent variables.
- y = ax
- y = x + 12
- y = -3x
- y = 3x
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 = -3x
GIVEN-
x1 = -3, y1 = 9, x2 = -2, y2 = 6, x3 = -1, y3 = 3, x4 = 0, y4 = 0, x5 = 1, y5 = -3, x6 = 2, y6 = -6, x7 = 3, y7 = -9
TO FIND-
Equation that matches the given coordinates
SOLUTION-
we observe that (-3,9) and (-2,6) 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-9)/ [(x-(-3)] = (6-9)/ [-2-(-3)]
∴ (y-9)/ (x+3) = -3/-2+3
∴ (y-9)/ (x+3) = -3/1
∴ 1 (y-9) = -3 (x+3) ...................... (Cross multiplying)
∴ y - 9 = -3x - 9
∴ y = -3x - 9 + 9 ....................... (Adding both sides with 9)
∴ y = -3x
FINAL ANSWER-
Option 'c' i.e. 'y = -3x' is the correct answer to the given question.
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