How do you find the slope that is perpendicular to the line #4x-3y = -24#?

1 Answer
Apr 29, 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)#

Our equation is: #color(red)(4)x - color(blue)(3)y = color(green)(-24)#

Therefore the slope of the line in the equation is:

#m = (-color(red)(4))/color(blue)(-3) = 4/3#

Let's call the slope of a line perpendicular to the line in the problem:

#m_p#

The formula for a perpendicular line is:

#m_p = -1/m#

Substituting the slope we calculated for #m# gives:

#m_p = -1/(4/3) = -3/4#