How do you find the slope that is perpendicular to the line #5x + 2y = 6#?

1 Answer
Apr 26, 2017

Answer:

See the solution process below.

Explanation:

This equation is in Standard Form for a linear equation. 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)#

Therefore the slope of #color(red)(5)x + color(blue)(2)y = color(green)(6)# is:

#m = -color(red)(5)/color(blue)(2)#

Let the slope of the perpendicular line be: #m_p#

The formula for the slope of a perpendicular line is:

#m_p = -1/m#

Substituting gives:

#m_p = (-1)/(-5/2) = 2/5#