Question

The equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither.

$y=\frac{1}{2}x+4;$$2x+4y=1$

Short answer

Given lines areneither parallel nor perpendicular.

Step-by-step solution

Step 1. Definition of the slope-intercept form.

Point-intercept is the equation of a straight line in the form$y=mx+b$, where m is the slope and b is y-intercept.

Step 2. Find the slope of y=12x+4.

We have$y=\frac{1}{2}x+4$

Compare with slope-intercept form, we get

$m_1=\frac{1}{2}$

Step 3. Find the slope of 2x+4y=1.

We have$2x+4y=1$

Subtract 2x to the both sides of the equation:

$\begin{array}{l}2x+4y-2x=1-2x\\ 4y=-2x+1\end{array}$

Divide both sides by 4:

$\begin{array}{l}\frac{4y}{4}=\frac{-2x+1}{4}\\ y=-\frac{1}{2}x+\frac{1}{4}\end{array}$

Compare with slope-intercept form, we get

$m_2=-\frac{1}{2}$

So, both the given lines are neither parallel nor perpendicular since their slopes are neither equal nor negative reciprocals of each other.