## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

If two non-vertical and non-horizontal lines are parallel, then their slopes are equal. If two non-vertical and non-horizontal lines are perpendicular, the product of their slopes is $-1$. Here, for the first line: $y=\frac{1}{2}x-3$ The slope, in this form of the equation, is equal to the coefficient of $x$. Hence, the slope of this line $\frac{1}{2}$. For the second line: $y=-2x+4$ The slope of this line is $-2$. Since $\frac{1}{2} \times -2=-1$, then the two lines are perpendicular.