Question

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

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

Short answer

Neither parallel nor perpendicular.

Step-by-step solution

Step 1. Given information

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

Step 2. Solve for y.

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

$\begin{array}{rcl}2x-4y& =& 6\\ -4y& =& 6-2x\\ \frac{-4y}{-4}& =& \frac{6-2x}{-4}\\ y& =& -\frac{3}{2}+\frac{1}{2}x\end{array}$

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

Step 3. Determine slope and y- intercepts.

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

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

• The y-intercept of first and second line is $\left(0,-\frac{3}{2}\right)$and $\left(0,-\frac{3}{2}\right)$respectively.

Step 4. Conclusion

Since both the lines have same slope and same values of y-intercepts, so they are neither parallel nor perpendicular to each other.