Question

Determine whether the lines are parallel, perpendicular, or neither. y= -2x+5
y= 1/2x+3

Answer 1

The answer is neither. This system is has one solution. Both the slope and y-intercept are different.

Explanation:

Answer 2

`Let\ k:y=m_1x+b_1\ and\ l:y=m_2x+b_2,\ then:\\\\l\ ||\ k\iff m_2=m_1\\\\l\ \perp\ k\iff m_2m_1=-1\\---------------------------\\\text{We have}\\\\y=-2x+5\to m_1=-2\\\\y=(1)/(2)x+3\to m_2=(1)/(2)\\\\m_2\\eq m_1\to \text{the lines are not parallel}\\\\m_2m_1=(1)/(2)(-2)=-1\to\text{the lines are perpendicular}\\\\Answer:\ \boxed{\text{The lines are perpendicular}}`