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

1 Answer
Mar 12, 2018

Answer:

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#