complete the table below

input x 0 1 2 3 4 5
output y 4 10 16 22
and an equation to show the relationship

looks like your y values increase by 6 for every increase in the x

so it must by
y = 6x + b
put in one of the pairs, e.g.( 2,16)
16 = 12 + b
b = 4

y = 6x + 4

To complete the table, we need to find the missing values in the "y" column. Let's examine the pattern between the input "x" values and the output "y" values.

From the given data, we can observe that the "y" values are increasing by 6 each time. Let's calculate the difference between consecutive "y" values:

y(1) - y(0) = 10 - 4 = 6
y(2) - y(1) = 16 - 10 = 6
y(3) - y(2) = 22 - 16 = 6

Therefore, we can conclude that the common relationship between the "x" and "y" values is that the "y" values increase by 6 for each increase in "x" by 1.

Now, to find the missing "y" values in the table:

y(0) + 6 = 4 + 6 = 10
y(1) + 6 = 10 + 6 = 16
y(2) + 6 = 16 + 6 = 22

The completed table would be as follows:
input x 0 1 2 3 4 5
output y 4 10 16 22 28 34

To represent this relationship with an equation, we can consider the general form of a linear equation: y = mx + b, where "m" is the slope and "b" is the y-intercept.

From the pattern we observed, we can see that for each increase in "x" by 1, the corresponding "y" value increases by 6. Therefore, the slope "m" is 6.

Since the table starts with "y" at 4 when "x" is 0, the y-intercept "b" is 4.

Thus, the equation showing the relationship between "x" and "y" is y = 6x + 4.