Question

What is an equation of the line that passes through the point ( − 6 , − 2 ) (−6,−2) and is parallel to the line 3 x − 2 y = 2 ?

Answer 1

Explanation:

let's rearrange the equation 3 x − 2 y = 2 a bit. (isolate y)

3x - 2 /2 = 2y /2

(3x-2)/2 = y

`(3)/(2) x` - 1 = y

The slope for the equation is 3/2.

Rule: Parallel lines have the same slope

So we know that the slope of the line we need to find is 3/2.

y = mx +b

y = (3/2)(x) + b

Now plug in the point (-6,-2) to find b

-2 = (3/2)(-6) + b

-2 = -9 + b

-2 + 9 = -9 + b + 9

7 = b

b = 7

Therefore the equation of the line we need to find: y =
`(3)/(2)x + 7`