Table A, B and D are represents a linear function.
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
There are 4 tables.
Now,
For Table A;
The equation of line is,
⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)
⇒ y - 5 = (2 - 5) / (- 1 - (-2)) (x - (-2))
⇒ y - 5 = - 3/1 (x + 2)
⇒ y - 5 = - 3 (x + 2)
⇒ y - 5 = - 3x - 6
⇒ y = - 3x - 1
For Table B;
The equation of line is,
⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)
⇒ y - 5 = (3 - 5) / (- 1 - (-2)) (x - (-2))
⇒ y - 5 = - 2/1 (x + 2)
⇒ y - 5 = - 2 (x + 2)
⇒ y - 5 = - 2x - 4
⇒ y = - 3x + 1
For Table C;
The equation of line is,
⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)
⇒ y - (-2) = (- 1 - (-2)) / (3 - 3) (x - 3)
⇒ y + 2 = 1/0 (x + 2)
⇒ y - 5 = ∞
Hence, It is not possible.
For Table D;
The equation of line is,
⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)
⇒ y - 0 = (-1 - 0) / ( 1 - 0) (x - 0)
⇒ y - 0 = - 1/1 (x)
⇒ y = - x
Thus, Table A, B and D are represents a linear function.
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