Question

Ne that goes through the point (-1,1) and is parallel to the line -5x-4y=-8

Answer 1

y = (-5/4)x - 1/4

Explanation:

Parallel lines have the same slope

-5x - 4y = -8

Change to slope-intercept form

-4y = 5x - 8

y = (-5/4)x + 2

the slope is -5/4

y = mx + b

substitute the point (-1,1) and slope

1 = (-5/4)(-1) + b

1 = 5/4 + b

1 - 5/4 = b

-1/4 = b

y = (-5/4)x - 1/4

Answer 2

5x + 4y = - 1

Explanation:

the equation of a line in slope- intercept form is

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

given

- 5x - 4y = - 8 ( add 5x to both sides )

- 4y = 5x - 8 ( divide through by - 4 )

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

with slope m = -
`(5)/(4)`

• Parallel lines have equal slopes , then

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

to find c substitute (- 1, 1 ) into the partial equation

1 = -
`(5)/(4)` (- 1) + c =
`(5)/(4)` + c ( subtract
`(5)/(4)` from both sides )

1 -
`(5)/(4)` = c , then

c =
`(4)/(4)` -
`(5)/(4)` = -
`(1)/(4)`

y = -
`(5)/(4)` x -
`(1)/(4)` ← equation of parallel line in slope- intercept form

multiply through by 4 to clear the fractions

4y = - 5x - 1 ( add 5x to both sides )

5x + 4y = - 1 ← equation of parallel line in standard form