Question

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

Answer 1

`(-1/2)`.

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 = (6)/(7)`.

`\displaystyle -y = -2\, x + (6)/(7)`.

`\displaystyle y = 2\, x - (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) = -(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) &= -(1)/(m_(1)) \\ &= -(1)/(2)\end{aligned}`.