Question

What is the slope of a line parallel and perpendicular to 6x + 4y = -4?

Answer 1

See the 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)`

A line parallel to this line will have the same slope as:

`color(red)(6)x + color(blue)(4)y = color(green)(-4)`

`m = -color(red)(6)/color(blue)(4) = -3/2`

Let us call the slope of the perpendicular line `m_p`.

The formula for the slope of a perpendicular line is:

`m_p = -1/m`

Substituting gives the slope of the perpendicular line as:

`m_p = -1/(-3/2) = 2/3`