Question

what is the correct classification for the following two linear equations?-2x + y =3y = -1/2 x-2A. Parallel Lines B. Perpendicular Lines

Answer 1

we are given the two linear equations

First Equation

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

Second Equation

`y=-(1)/(2)x-2`

Let mA and mB denotes the gradient of the first and second equation respectively written as

`m_A\text{ and }m_B`

Using the slope - intercepty form, one can see that

`\begin{gathered} m_A=2 \\ \\ m_B=-(1)/(2) \end{gathered}`

Now,

`\begin{gathered} m_A* m_B=2*-(1)/(2) \\ \\ m_A* m_B=-1 \end{gathered}`

Therefore, the lines are Perpendicular

Option B