Question

In the following exercise, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.

$2x+4y=3$;$6x+3y=2$

Short answer

Neither parallel nor perpendicular.

Step-by-step solution

Step 1. Given information

The given equations are$2x+4y=3$and$6x+3y=2$.

Step 2. Solve for y.

Solve both the equations to obtain the value of y in terms of x.

$\begin{array}{rcl}2x+4y& =& 3\\ 4y& =& 3-2x\\ \frac{4y}{4}& =& \frac{3-2x}{4}\\ y& =& \frac{3}{4}-\frac{1}{2}x\end{array}$

$\begin{array}{rcl}6x+3y& =& 2\\ 3y& =& 2-6x\\ \frac{3y}{3}& =& \frac{2-6x}{3}\\ y& =& \frac{2}{3}-2x\end{array}$

Step 3. Determine slopes

• Now both equations are in slope-intercept form.
• Determine the slopes $m_1$and $m_2$by comparing both equations with $y=mx+b$.

$\begin{array}{rcl}{m}_1& =& -\frac{1}{2}\\ m_2& =& -2\end{array}$

• The obtained slopes are neither same nor negative reciprocal of each other. So, the given lines are neither parallel nor perpendicular.