How do you find the slope that is perpendicular to the line #3x-5y=-8#?

1 Answer
May 25, 2017

Answer:

See a 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

#color(red)(3)x - color(blue)(5)y = color(green)(-8)#

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

Substituting and calculating #m# gives:

#m = color(red)(-3)/color(blue)(-5) = 3/5#

Let's call the slope of the perpendicular line: #m_p#

The formula to find the slope of a perpendicular line is:

#m_p = -1/m#

Substituting the slope we calculated above gives:

#m_p = -1/(3/5)#

#m_p = -5/3#