The equation for line v can be written as y+6= – (x+4). Line w includes the point ( – 2, – 1) and is parallel to line v. What is the equation of line w?

Question

The equation for line 

v

 can be written as 

y

+

6

=

–

(

x

+

4

)

.

 Line 

w

 includes the point 

(

–

2

,

–

1

)

 and is parallel to line 

v

.

 What is the equation of line 

w

?

Answer 1

OK, so line v is graphed as y + 6 = - (x + 4) which can be simplified as follows:

y + 6 - 6 = - (x + 4) - 6

y = - x - 4 - 6

y = - (x + 10)

y = -1(x + 10) where 10 is the constant in the equation and -1 is the slope for line v.

So, for parallel line w, the slope will be exactly the same. Only the constant will differ.

Plugging in the point (-2, -1) gives the following equation for line w:

-1 = -1((-2) + c) where c is the new constant for parallel line w

-1 = - (-2 + c)

-1 = 2 - c

3 = c

Replace the constant 10 in y = -1 (x + 10) for line v with "3" and you get

y = -1 (x + 3) or

y = - (x+3)

This equation is equal to the equation in the first answer you were given, as follows:

y = - (x+3)

y+1 = - (x+3) +1

y+1 = - x - 3 + 1

y+1 = - x - 2

y+1 = - (x+2)

This method is much longer than the first!! But I did it this way in case it helps you see "why" the point-slope method works.

Answer 2

Parallel lines have the same slope. So, using the point-slope form of a linear equation:

y - (-1) = - (x - (-2))

or

y + 1 = - ( x + 2 )