Question

Which of these statements is true about the graphs of the equations below? y = 2x + 6 3y = 6x - 6

Answer 1

The lines are parallel

Step-by-step explanation:

Given the equations;

`\begin{gathered} y=2x+6------1 \\ 3y=6x-6------2 \end{gathered}`

To simplify equation 2, let us divide equation 2 through by 3;

`\begin{gathered} (3y)/(3)=(6x)/(3)-(6)/(3) \\ y=2x-2-------------2a \end{gathered}`

Comparing equation 1 to equation 2a;

`\begin{gathered} y=2x+6-------1 \\ y=2x-2-------2a \end{gathered}`

The slope of the equations are;

`\begin{gathered} y=mx+b \\ m_1=2 \\ m_(2a)=2 \end{gathered}`

Since the slope of the two equations are both equal to 2 ( equal), then the lines of the equations will be parallel.

Therefore, The lines are parallel