Answer:
Option (1) The first table represents a linear function
The first one from the left side
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Step-by-step explanation:
The general equation of the linear function is as following
y = mx + c
Where m is the slope and c is constant
The slope m = Δy/Δx
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For the first table: find the slope using the first two points (1, 1/2) and (2,1)
m = (1 - 1/2)/(2-1) = 0.5 ⇒(1)
Check the value using the second two points (3,1.5) and (4,2)
m = (2-1.5)/(4-3) = 0.5 ⇒(2)
From (1) and (2)
The first table represents a linear function
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For the second table:
We can note that for each row the value of y is reciprocal of the value of x
Which mean that x * y = 1
And this equation doesn't represent a linear function.
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For the third table:find the slope using the first two points (1,7) and (2,9)
m = (9-7)/(2-1) = 1 ⇒(1)
Check the value using the second two points (3,13) and (4,21)
m = (21-13)/(4-3) = 8 ⇒(2)
From (1) and (2)
The third table doesn't represent a linear function.
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For the fourth table:find the slope using the first two points (1,0) and (2,6)
m = (6-0)/(2-1) = 6 ⇒(1)
Check the value using the second two points (3,16) and (4,30)
m = (30-16)/(4-3) = 14 ⇒(2)
From (1) and (2)
The fourth table doesn't represent a linear function.
