Question

Which of the following equations is equivalent to y= -3x=4A. y= -3x + 4 B. y - 7 =3(x - 1) C. y- 10 = 3( x - 2) D. y - 10 = 3( x - 1)

Answer 1

Step 1

Rearrange the equation

`\begin{gathered} y-3x=4 \\ y=4+3x \end{gathered}`

Step 2

Test all options by rearrangement

Option A

`\begin{gathered} y=\text{ -3x +4} \\ \text{This is not equivalent to the given equation} \end{gathered}`

Option B

`\begin{gathered} y-7=3(x-1) \\ y=3x-3+7 \\ y=3x+4 \\ y=\text{ 4 + 3x} \\ \text{Hence option B is an equivalent} \end{gathered}`

Option C

`\begin{gathered} y-10=3(x-2) \\ y=\text{ 3x-6+10} \\ y=\text{ 3x +4} \\ y=\text{ 4+3x} \\ \text{Hence option C is equivalent} \end{gathered}`

Option D

`\begin{gathered} y-10=3(x-1) \\ y=\text{ 3x-3+10} \\ y=\text{ 3x+7} \\ y=\text{ 7+3x} \\ \text{Hence option D is not equivalent} \end{gathered}`

Hence, the equivalent options to the equation are options B and C