Question

What is the equation of a line that is parallel to 2x + 3y = 3 and passes through the point (3, -4)?

Enter your answer as a slope intercept equation (y=mx+b) in the box.​

Answer 1

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

Explanation:

the equation of a line in slope- intercept form is

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

given

2x + 3y = 3 ( subtract 2x from both sides )

3y = - 2x + 3 ( divide through by 3 )

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

with slope m = -
`(2)/(3)`

• Parallel lines have equal slopes , then

y = -
`(2)/(3)` x + b ← is the partial equation

to find b substitute (3, - 4 ) into the partial equation

- 4 = - 2 + b ⇒ b = - 4 + 2 = - 2

y = -
`(2)/(3)` x - 2 ← equation of parallel line