Question

What is the equation of the line that is parallel to 8x-5y=2 and goes through the point (-5,-2)

Answer 1

8x - 5y = - 30

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 8x - 5y = 2 into this form

Subtract 8x from both sides

- 5y = - 8x + 2 ( divide all terms by - 5 )

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

with slope m =
`(8)/(5)`

• Parallel lines have equal slopes, hence

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

To find c substitute (- 5, - 2) into the partial equation

- 2 = - 8 + c ⇒ c = - 2 + 8 = 6

y =
`(8)/(5)` x + 6 ← in slope- intercept form

Multiply through by 5

5y = 8x + 30 ( subtract 5y from both sides )

0 = 8x - 5y + 30 ( subtract 30 from both sides )

8x - 5y = - 30 ← in standard form