Question

Help! It says that I need to determine If both equations represent lines which are parallel, perpendicular, or none...

Answer 1

    4x + 2y = 8     (1)
    8x + 4y = -4y  (2)

A) Two lines are parallel if they have the same gradient
       - putting both equations into the gradient- intercept form ( y = mx + c                where m is the gradient)
            (1) 4x + 2y = 8
                          2y = 8 - 4x
                            y = -2x + 4
             
            (2) 8x + 4y = -4y
                          8x = -4y - 4y
                            y = $\frac{-8x}{-8}$
                            y = -x
   Thus the gradient of the two equations are different and as such          the two lines are not parallel

B)  When two lines are perpendicular, the product of their gradient is -1
                   $m_{1} * m_{2} = p$
                                             p = (-2) * (-1)
                                             p =  2
          ∴ the two lines are not perpendicular either.

Thus these lines are SKEWED LINES