How do you find the slope that is perpendicular to the line # 9x-y=9#?

2 Answers
May 24, 2018

Answer:

Slope of line, perpendicular to the line, # 9 x -y = 9 # is
# -1/9#.

Explanation:

Slope of the line, # 9 x -y = 9 or y= 9 x - 9 ; [y=mx+c]#

is #m_1= 9 # [Compared with slope-intercept form of equation]

The product of slopes of the perpendicular lines is #m_1*m_2=-1#

#:.m_2=(-1)/9= -1/9#. Therefore slope of the line, perpendicular

to the line, # 9 x -y = 9 # is # -1/9# [Ans]

May 24, 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

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

#color(red)(9)x - y = color(green)(9)#

#color(red)(9)x + color(blue)(-1)y = color(green)(9)#

Therefore, the slope for this line is:

#m = (-color(red)(9))/color(blue)(-1) = 9#

Let's call the slope of a perpendicular line: #color(blue)(m_p)#

The slope of a line perpendicular to a line with slope #color(red)(m)# is the negative inverse, or:

#color(blue)(m_p) = -1/color(red)(m)#

Substituting the slope for the line in the problem gives:

#color(blue)(m_p) = (-1)/color(red)(9) = -1/9#