Question

Given the line 5x – 4y = 9, give the equation of a line parallel and passing through (9, 5).

Answer 1

5x - 4y = 25

Explanation:

the equation of a line in slope- intercept form is

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

given the line

5x - 4y = 9 ( subtract 5x from both sides )

- 4y = - 5x + 9 ( divide through by - 4 )

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

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

• Parallel lines have equal slopes , then

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

to find c substitute (9, 5 ) into the partial equation

5 =
`(5)/(4)` (9) + c =
`(45)/(4)` + c ( subtract
`(45)/(4)` from both sides )

-
`(25)/(4)` = c

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

multiply through by 4 to clear the fractions

4y = 5x - 25 ( subtract 5x from both sides )

- 5x + 4y = - 25 ( multiply through by - 1 )

5x - 4y = 25 ← equation of parallel line in standard form