Question

What is the slope of the line perpendicular to the line 14x-7y=6

Answer 1

Answer:

$(-1/2)$.

Step-by-step explanation:

In a cartesian plane, if the equation of a line is in the slope-intercept form $y = m\, x + b$, then $m$ would be the slope of that line.

Rewrite the equation of the given line to obtain the slope-intercept equation for this line:

$\displaystyle 2\, x - y = \frac{6}{7}$.

$\displaystyle -y = -2\, x + \frac{6}{7}$.

$\displaystyle y = 2\, x - \frac{6}{7}$.

In other words, the slope of the given line is $2$.

Let $m_{1}$ denote the slope of the given line, and let $m_{2}$ denote the slope of the line perpendicular to the given line.

If two lines in a cartesian plane are perpendicular to one another, the product of their slopes would be $(-1)$. In other words, $m_{1} \cdot m_{2} = -1$. Rearrange to obtain an expression for the slope of the line perpendicular to the given line:

$\displaystyle m_{2} = -\frac{1}{m_{1}}$.

The slope of the given line has been found: $m_{1} = 2$. Hence, the slope of the line perpendicular to this given line would be:

$\begin{aligned}m_{2} &= -\frac{1}{m_{1}} \\ &= -\frac{1}{2}\end{aligned}$.