Which table represents a linear function

Answer:

Option (1) The first table represents a linear function

The first one from the left side

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

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

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.

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.

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.

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870