Question

Find an equation of the line that passes through (-5,-7) and is parallel to 5x+9y+18=0. Give answer in slope intercept form

Answer 1

y = -
`(5)/(9)` x -
`(88)/(9)`

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange 5x + 9y + 18 = 0 into slope- intercept form

Subtract 5x + 18 from both sides

9y = - 5x - 18 ( divide all terms by 9 )

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

with m = -
`(5)/(9)`

Parallel lines have equal slopes, thus

y = -
`(5)/(9)` x + c ← is the partial equation

To find c substitute (- 5, - 7) into the partial equation

- 7 =
`(25)/(9)` + c ⇒ c = - 7 -
`(25)/(9)` = -
`(88)/(9)`

y = -
`(5)/(9)` x -
`(88)/(9)` ← equation of line