Question

Which equation expresses the relationship between the pairs of values of X and why shown in the table below

Answer 1

We are given a table that relates values of "x" and values of "y". To determine which equation expresses the relationship we need to substitute the values of "x" and we should get the values of "y". We will begin with x = 1. For the first equation we have:

`y=3x-2`

Substituting x = 1 we get:

`\begin{gathered} y=3(1)-2 \\ y=3-2 \\ y=1 \end{gathered}`

Therefore, this is a possible solution. Now for the second equation, we get:

`y=2x`

Substituting the value we get:

`\begin{gathered} y=2(1) \\ y=2 \end{gathered}`

We got 2 instead of 1 as shown in the table, therefore, we can discard this equation as a possible solution.

Now, we use the third equation:

`y=2x+1`

Substituting the value we get:

`\begin{gathered} y=2(1)+1 \\ y=2+1 \\ y=3 \end{gathered}`

We got 3 instead of 1, therefore, we can discard this equation as a possible solution.

Now the fourth equation:

`y=x`

Substituting the value we get:

`y=1`

Therefore, this is also a possible solution.

Now we use the value x = 2, we will substitute in the first and fourth equations which are the ones we haven't discarded yet. For the first equation we get:

`\begin{gathered} y=3(2)-2 \\ y=6-2 \\ y=4 \end{gathered}`

Therefore, this is a possible solution. Now for the fourth equation:

`y=2`

We got 2 instead of 4, therefore, this is not a solution, therefore, the right equation must be the first equation. To be sure we can replace the remaining values of "x" and we should get the corresponding values of "y".