Question

What is an equation of the line that passes through the point

(−6,−8) and is parallel to the line
x−2y=6?

Answer 1

x - 2y = 10

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x - 2y = 6 ( subtract x from both sides )

- 2y = - x + 6 ( divide both sides by - 2 )

y =
`(1)/(2)` x - 3 ← in slope- intercept form

with slope m =
`(1)/(2)`

Parallel lines have equal slopes, thus

y =
`(1)/(2)` x + c ← is the partial equation

To find c substitute (- 6, - 8) into the partial equation

- 8 = - 3 + c ⇒ c = - 8 + 3 = - 5

y =
`(1)/(2)` x - 5 ← in slope- intercept form

Multiply through by 2

2y = x - 10 ( subtract 2y from both sides )

0 = x - 2y - 10 ( add 10 to both sides )

10 = x - 2y, that is

x - 2y = 10 ← in standard form