Question

A line contains the point (-2, 2) and is parallel to the line y = ½x + 8. What is the equation of this parallel line?

Answer 1

y =
`(1)/(2)` x + 3

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 with equation

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

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

• Parallel lines have equal slopes , then

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

to find c, substitute the point (- 2, 2 ) into the partial equation

2 =
`(1)/(2)` (- 2) + c = - 1 + c ( add 1 to both sides )

3 = c

y =
`(1)/(2)` x + 3 ← equation of parallel line