Question

Find the equation of the line parallel to H passes through (-4,2)

Answer 1

y =
`(1)/(3)` x +
`(10)/(3)`

Explanation:

The equation of a line in slope- intercept form is

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

Calculate the slope m of H using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (3, - 2) ← 2 points on the line

m =
`(-2+3)/(3-0)` =
`(1)/(3)`

Parallel lines have equal slopes, thus

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

To find c substitute (- 4, 2) into the partial equation

2 = -
`(4)/(3)` + c ⇒ c = 2 +
`(4)/(3)` =
`(10)/(3)`

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