Question

Find the equation of the line which passes through the point (3,−4), and is parallel to the line with the equation y=1/2x+3/2. Express your answer in slope-intercept form. Simplify your answer.

Answer 1

y =
`(1)/(2)` x -
`(11)/(2)`

Explanation:

the equation of a line in slope- intercept form is

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

given

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

with slope m =
`(1)/(2)`

• Parallel lines have equal slopes , then

y =
`(1)/(2)` x + c ← is the partial equation

to find c substitute (3, - 4 ) into the partial equation

- 4 =
`(1)/(2)` (3) + c =
`(3)/(2)` + c ( subtract
`(3)/(2)` from both sides )

- 4 -
`(3)/(2)` = c , then

c = -
`(8)/(2)` -
`(3)/(2)` = -
`(11)/(2)`

y =
`(1)/(2)` x -
`(11)/(2)` ← equation of parallel line