Questions: Fill in each blank so that the resulting statement is true. Consider the line whose equation is 7x + y - 6 = 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 (Type an integer or a simplified fraction.)

$Fill in each blank so that the resulting statement is true. Consider the line whose equation is 7x + y - 6 = 0. The slope of any line that is parallel to this line is . The slope of any line that is perpendicular to this line is . The slope of any line that is parallel to this line is (Type an integer or a simplified fraction.)$

Transcript text: Fill in each blank so that the resulting statement is true Consider the line whose equation is $7 x+y-6=0$. The slope of any line that is parallel to this line is $\qquad$ The slope of any line that is perpendicular to this line is $\qquad$ - The slope of any line that is parallel to this line is $\square$ (Type an integer or a simplified fraction.)

Solution

Solution Steps

Step 1: Find the slope of the line parallel to the given line

To find the slope of a line parallel to the given line $ax + by + c = 0$, we rearrange the equation into the slope-intercept form $y = mx + b$, where $m$ is the slope. For the given equation, the slope ($m$) is $-\frac{a}{b} = -\frac{7}{1}$. Therefore, the slope of any line parallel to the given line is $-7$.

Step 2: Find the slope of the line perpendicular to the given line

The slope of any line perpendicular to the given line is the negative reciprocal of the slope of the given line. If the slope of the given line is $m$, then the slope of a line perpendicular to it is $-\frac{1}{m}$. For the given form $ax + by + c = 0$, the slope of a perpendicular line is $\frac{b}{a} = \frac{1}{7}$. Therefore, the slope of any line perpendicular to the given line is $0.14$.