How do you tell whether the lines for each pair of equations are parallel, perpendicular, or neither: #y=(-1/5)x+6, -2x+10y=5#?

1 Answer
Dec 11, 2016

Answer:

They are neither parallel nor perpendicular.

Explanation:

Given -

#y=(-1/5)x+6# -------------------------(1)
#-2x+10y=5#---------------------------(2)

The first line equation is in the slope intercept form

#y=mx+c#

The slope #m_1# of the 1st line is #=-1/5#

The second line is in the form

#ax+by=c#

In this case, slope is defined by #-a/b#

Applying this formula, the slope #m_2# of the second line #=-(-2)/10=1/5#

Then apply these conditions to decide the types of relation between the two lines.

If #m_1=m_2#, then the two lines are parallel to each other.
If the product of #m_1# and #m_2# is equal to #-1# , then the two lines are perpendicular to each other.

Otherwise, the two lines are neither parallel nor perpendicular.

In our case #m_1=-1/5# and #m_2=1/5# satisfy neither of the two conditions.

Hence they are neither parallel nor perpendicular.