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

2 Answers
Aug 25, 2017

Answer:

See a solution process below:

Explanation:

First, let's put the equation 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)#

#x = -5y - 5#

#x + color(red)(5y) = -5y + color(red)(5y) - 5#

#x + 5y = 0 - 5#

#color(red)(1)x + color(blue)(5)y = color(green)(-5)#

Substituting for #color(red)(A)# and #color(blue)(B)# gives the slope of this line as:

#m = -color(red)(1)/color(blue)(5)#

Now, let's call the slope for the line perpendicular to this #m_p#

The rule of perpendicular slopes is:

#m_p = -1/m#

Substituting the slope we calculated gives:

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

Aug 25, 2017

Answer:

Slope of line is # 5#

Explanation:

The slope of the line # x= -5y -5 or 5y = -x -5 or y = -x/5 -1# is

#m_1= -1/5 # [Compare with standard slope intercept form

#y=mx+c#] . We know the product of slopes of perpendicular

lines is #m*m_1=-1 :. m= -1/m_1= -1/(-1/5)= 5#

Slope of line perpendicular to the line # x= -5y -5# is # 5# [Ans]