# How do you find the slope of the line parallel to and perpendicular to #2y-x=7#?

##### 1 Answer

#### Answer:

The equation of the line parallel to the given line is -

#-x+2y=14#

The equation of the perpendicular line is -

#2x+y=7#

#### Explanation:

Given -

#2y-x=7#

Rewrite it as to suit our convenience.

#-x+2y=7#

The slope of the line is given by the formula

#m=(-a)/b#

Where -

#a-# is the coefficient of x

#b-# is the coefficient of y

The slope of the given line

For a line to be parallel, it also must have the same slope.

So it is enough if you change the value of the Constant term.

Let us replace 7 with 14. There is no hard and fast rule in assigning any other value. A line can have any number of parallel lines.

The equation of the line parallel to the given line is -

#-x+2y=14#

For a line to be perpendicular, the product of the slopes of the two lines must be equal to

There is short cut to find the equation of a perpendicular line.

Step 1

Interchange the coefficients of

#2x-1y=7#

Step 2

Change the sign of the

#2x+1y=7#

Now write the equation

The equation of the perpendicular line is -

#2x+y=7#

Its slope is

Find the product to acertain the correctness of your answer

#m_1 xx m_2=(-1)/2xx2=-1#

Hence the equation of the perpendicular line is correct.