Question

What is an equation of the line that passes through the point (3,−3) and is parallel to the line x+ 3y= 18

Answer 1

x + 3y = - 6

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 equation

x + 3y = 18 ( subtract x from both sides )

3y = - x + 18 ( divide through by 3 )

y = -
`(1)/(3)` x + 6 ← in slope- intercept form

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

• Parallel lines have equal slopes , then

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

to find c, substitute (3, - 3 ) for x and y into the partial equation

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

- 2 = c

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

multiply through by 3

3y = - x - 6 ( add x to both sides )

x + 3y = - 6 ← equation in standard form