Question

How do you find the slope that is perpendicular to the line `x - 5y = -10`?

Answer 1

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

`color(red)(1)x - color(blue)(5)y = color(green)(-10)`

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

Substituting gives the slope of the line in the problem as:

`m = -color(red)(1)/color(blue)(-5) = 1/5`

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

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

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

Substituting the slope for the line in the problem gives:

`color(blue)(m_p) = (-1)/color(red)(1/5) = -5`