Question

How do you find the slope that is perpendicular to the line `9x-y=9`?

Answer 1

Slope of line, perpendicular to the line, `9 x -y = 9` is
`-1/9`.

Explanation:

Slope of the line, `9 x -y = 9 or y= 9 x - 9 ; [y=mx+c]`

is `m_1= 9` [Compared with slope-intercept form of equation]

The product of slopes of the perpendicular lines is `m_1*m_2=-1`

`:.m_2=(-1)/9= -1/9`. Therefore slope of the line, perpendicular

to the line, `9 x -y = 9` is `-1/9` [Ans]

Answer 2

See a solution process below:

Explanation:

This equation is in Standard Linear Form. The standard form of a linear equation is: `color(red)(A)x + color(blue)(B)y = color(green)(C)`

Where, if at all possible, `color(red)(A)`, `color(blue)(B)`, and `color(green)(C)`are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

The slope of an equation in standard form is: `m = -color(red)(A)/color(blue)(B)`

`color(red)(9)x - y = color(green)(9)`

`color(red)(9)x + color(blue)(-1)y = color(green)(9)`

Therefore, the slope for this line is:

`m = (-color(red)(9))/color(blue)(-1) = 9`

Let's call the slope of a perpendicular line: `color(blue)(m_p)`

The slope of a line perpendicular to a line with slope `color(red)(m)` is the negative inverse, or:

`color(blue)(m_p) = -1/color(red)(m)`

Substituting the slope for the line in the problem gives:

`color(blue)(m_p) = (-1)/color(red)(9) = -1/9`