Q. 104 - Precalculus Enhanced with Graphing Utilities

Question

The equations of two lines are given. Determine if the lines are parallel, perpendicular, or neither. $y=\frac{1}{2}x-3$, $y=-2x+4$

Step-by-Step Solution

Answer

The given lines are perpendicular.

Step 1. Given information

Equations of two lines: $y=\frac{1}{2}x-3$, $y=-2x+4$

Step 2. Determining if the lines are parallel, perpendicular, or neither.

For the lines to be parallel, slopes should be equal and for the lines to be perpendicular, product of slopes is $-1$.

Slope-intercept form of the line is $y=mx+b$

For the given lines, product of slopes is $-1$, $m_1\times m_2=\frac{1}{2}\times -2=-1$.

Therefore, the given lines are perpendicular.