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

1 Answer
Apr 26, 2017

Answer:

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#