Question

Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3).

Answer 1

A) y = − 1 /5 x + 16/ 5

Explanation:

Answer 2

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange x + 5y = 10 into this form

Subtract x from both sides

5y = - x + 10 ( divide all terms by 5 )

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

with slope m = -
`(1)/(5)`

• Parallel lines have equal slopes, hence

y = -
`(1)/(5)` x + c ← is the partial equation of the parallel line

To find c substitute (1, 3) into the partial equation

3 = -
`(1)/(5)` + c ⇒ c =
`(16)/(5)`

y = -
`(1)/(5)` x +
`(16)/(5)` ← equation of parallel line