Which set of values could be from a direct proportion?

The value of k remains constant for table 2

Step-by-step explanation:

Given tables of X values and Y values

To find which tables show the property of direct proportional:

Since Y is direct proportion to X

We write,

y=kx     [Equation]

where k is constant of proportion.

Therefore, If the value of k remains constant for any table then, that table shows a direct proportion between y and x values.

For first table :

Now,

when x=1, y=3

Putting into Equation

y=kx

3=k(1)

k=3

Similarly, other calculations are carried out and put it into the form of a table

Note: Figure show tables of given and their respective k values.

Thus, the value of k remains constant for table 2

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

d is the answer

step-by-step explanation: