Question

fill in each blank so that the resulting statement is true. consider the line whose equation is $2x + y - 9 = 0$. the slope of any line that is parallel to this line is ____. the slope of any line that is perpendicular to this line is ____. the slope of any line that is parallel to this line is \boxed{} (type an integer or a simplified fraction.)

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $2x + y - 9 = 0$ to $y = mx + b$:
$y = -2x + 9$

Step2: Identify parallel slope

Parallel lines have equal slopes:
$m_{\text{parallel}} = -2$

Step3: Calculate perpendicular slope

Perpendicular slope is negative reciprocal:
$m_{\text{perpendicular}} = \frac{1}{2}$

Answer:

The slope of any line that is parallel to this line is $-2$.
The slope of any line that is perpendicular to this line is $\frac{1}{2}$.