Question

Which of the following equation(s) are equivalent to y − 4 = 2/3(x − 1)?Select all that apply.A.y = 2/3x − 10/3B.y = 2/3x + 3 1/3C.y = 2/3x + 3D.y = 2/3x + 10/3

Answer 1

We need to develop the given equation, isolate y on the left side, and then compare it to the equations in the options.

We have:

`\begin{gathered} y-4=(2)/(3)\mleft(x-1\mright) \\ \\ y-4=(2)/(3)x-(2)/(3) \\ \\ y=(2)/(3)x-(2)/(3)+4 \\ \\ y=(2)/(3)x-(2)/(3)+(12)/(3) \\ \\ y=(2)/(3)x+(10)/(3) \end{gathered}`

The above result is the same as shown in option D.

Also, we can rewrite 10/3 as:

`(10)/(3)=(9)/(3)+(1)/(3)=3+(1)/(3)=3(1)/(3)`

Therefore, another way of writing the original equation is:

`y=(2)/(3)x+3(1)/(3)`

Thus, option B is also correct.

Therefore, the correct options are B and D.