What is the slope of any line perpendicular to the line defined by the equation #y = -4x + 1#?

2 Answers
Aug 21, 2017

Answer:

See a solution process below:

Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

#y = color(red)(-4)x + color(blue)(1)#

Therefore, the slope of the line represented by the equation in the problem is:

#color(red)(m = -4)#

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

The slope of a perpendicular line is:

#m_p = -1/m#

Substituting gives:

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

Aug 21, 2017

Answer:

The slope is #1/4#

Explanation:

The perpendicular slope is expressed as the negative reciprocal of the slope or #-1/m#.

In this scenario, the slope, or #m#, is #-4# so the slope of the perpendicular line is #-1/(-4)# which simplifies to #1/4#