Question

Contains the point (-1, 2) and is parallel to
x – 2y = -3

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

Rearrange x - 2y = - 3 into this form

Subtract x from both sides

- 2y = - x - 3 ( divide all terms by - 2 )

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

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

• Parallel lines have equal slopes, thus

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

To find c substitute (- 1, 2) into the partial equation

2 = -
`(1)/(2)` + c ⇒ c = 2 +
`(1)/(2)` =
`(5)/(2)`

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

Multiply through by 2

2y = x + 5 ( subtract 2y from both sides )

0 = x - 2y + 5 ( subtract 5 from both sides )

- 5 = x - 2y, thus

x - 2y = - 5 ← in standard form