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:

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

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

Also, we can rewrite 10/3 as:

$\frac{10}{3}=\frac{9}{3}+\frac{1}{3}=3+\frac{1}{3}=3\frac{1}{3}$

Therefore, another way of writing the original equation is:

$y=\frac{2}{3}x+3\frac{1}{3}$

Thus, option B is also correct.

Therefore, the correct options are B and D.