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

Solution

we are given the two linear equations

First Equation

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

Second Equation

$y=-\frac{1}{2}x-2$

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

$\begin{gathered} m_A=2 \\ \\ m_B=-\frac{1}{2} \end{gathered}$

Now,

$\begin{gathered} m_A\times m_B=2\times-\frac{1}{2} \\ \\ m_A\times m_B=-1 \end{gathered}$

Therefore, the lines are Perpendicular

Option B