Question

Given the line x + 3y = 6 find the equation of the parallel line to this line through the point (3, 2) using point-slope form

Answer 1

y - 2 = -
`(1)/(3)` (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

x + 3y = 6 ( subtract x from both sides )

3y = - x + 6 ( divide through by 3 )

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

with slope m = -
`(1)/(3)`

• Parallel lines have equal slopes

then the slope of a parallel line is m = -
`(1)/(3)`

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = -
`(1)/(3)` and (a, b ) = (3, 2 ) , then

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