How do you find the slope that is perpendicular to the line #2x – 5y = 3#?

First, this line 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

#color(red)(2)x - color(blue)(5)y = color(green)(3)#

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

Substituting the values from the equation gives the slope of this line as:

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

The slope of a perpendicular line is the negative inverse of the slope.

So, if we can the slope of the perpendicular line #m_p# it's slope would be:

#m_p = -1/m#

Substituting the slope we calculated and calculating the perpendicular slope gives:

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

The slope of any line perpendicular to the line in the problem will have a slope of:

#-5/2#

Any linear equation in standard form: #Ax+By=C#
has a slope of #m=-A/B#
#rArr 2x-5y=3#
has a slope of #m=2/5#

The perpendicular to a line with a slope of #m#
has a slope of #-1/m#
#rArr# any perpendicular to #2x-5y=3#
has a slope of #-5/2#