Question

Which of the following ordered pairs is a solution of the line y-2x = 6? (2.2) (0, -3) (-3,0) (1.-3)

Answer 1

Step-by-step explanation

An ordered pair is a solution of a line if it "satisfies" the equation of the line. What does "satisfy" mean? It means that evaluating the pair for the point doesn't give a contradiction, but a true equality.

Now, let's test the first ordered pair:

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

Note that after evaluating the equation of our line for (2,2) we got a contradiction: -2 is not equal to 6. This means that (2,2) is not a solution to our line.

Let's test (0,-3):

`\begin{gathered} -3-2(0)=6, \\ -3+0=6, \\ -3=6. \end{gathered}`

Again we got a contradiction. (0,-3) is not a solution to our line.

Let's test (-3,0):

`\begin{gathered} 0-2(-3)=6, \\ 0+2(3)=6,\leftarrow\text{`

We got something true (6 is equal to itself).

Answer

The ordered pair from the options that is a solution of our line is

`(-3,0)\text{.}`