Question

Find an equation of the line passing through (-3, 2) and parallel to the graph of x - 2y = 7. Write the equation in slope-intercept form.

Answer 1

y =
`(1)/(2)` x +
`(7)/(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

x - 2y = 7 ( subtract x from both sides )

- 2y = - x + 7 ( multiply through by - 1 )

2y = x - 7 ( divide through by 2 )

y =
`(1)/(2)` x -
`(7)/(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, 2 ) into the partial equation

2 =
`(1)/(2)` (- 3) + c = -
`(3)/(2)` + c ( add
`(3)/(2)` to both sides )

2 +
`(3)/(2)` = c , that is

c =
`(7)/(2)`

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