Question

How do you find the slope that is perpendicular to the line `-15 +3y = -12x`?

Answer 1

See a solution process below:

Explanation:

First, we need to find the slope of the line in the problem. We can transform this equation into 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

`-15 + color(red)(15) + color(blue)(12x) + 3y = color(blue)(12x) - 12x + color(red)(15)`

`0 + 12x + 3y = 0 + 15`

`12x + 3y = 15`

`(12x + 3y)/color(red)(3) = 15/color(red)(3)`

`(12x)/color(red)(3) + (3y)/color(red)(3) = 5`

`color(red)(4)x + color(blue)(1)y = color(green)(15)`

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

Therefore, the slope of the line in the problem is:

`m = -color(red)(4)/color(blue)(1) = -4`

Let's call the slope of a perpendicular line: `m_p`

The slope of a perpendicular line is the negative inverse of the slope of the line it is perpendicular to.:

`m_p = -1/m`

Substituting gives:

`m_p = -1/-4 = 1/4`