Question

Write an equation that is parallel to the line 2x - 3y = 9 and passes through the point (4, -1).

A) y =
2
3
x -
11
3
B) y =
3
2
x -
11
3
C) y =
2
3
x +
11
3
D) y = −
2
3
x -
11
3

Answer 1

Answer:
`y = (2x)/(3) - (11)/(3)`

Explanation:

Equation of the line given ;

`2x - 3y = 9`

To find the slope of the line we will make y the subject of formula , that is

`3y = 2x - 9`

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

Therefore ; the slope =
`(2)/(3)`

Two lines are said to be parallel if they have the same slope

This means that the slope of the second line =
`(2)/(3)`

Using the formula
`y-y_(1)= m ( x - x_(1) )` to find the equation of the line , we have

`y - (-1 ) = (2)/(3) (x - 4 )`

`y + 1 = (2x)/(3) -(2)/(3)(4)`

`y + 1 = (2x)/(3) - (8)/(3)`

`y = (2x)/(3)- (8)/(3) - 1`

`y = (2x)/(3) - (11)/(3)`