Question

What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = –6?

y=-3/2x+8
y=3/2x-4
y=1/2x
y=2/3x-4

Answer 1

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

Explanation:

the equation of the line that passes through (4, 2) and is parallel to

3x – 2y = –6

Given equation of a line is
`3x-2y=-6`

Lets find the slope of the given line. Slope intercept form is

y=mx+b , where m is the slope

`3x-2y=-6`, subtract 3x on both sides

`-2y=-3x-6`

Divide whole equation by -2

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

the slope of the given equation is
`(3)/(2)`

Slope of parallel line is same as the slope of the given line

the slope of the parallel line is
`(3)/(2)`

now we use point (4,2)

Use point slope form of a line

`y=y1=m(x-x1)`, where (x1,y1) is the given point and m is the slope

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

`y-2=(3)/(2)x-6`

Add 2 on both sides

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

Answer 2

The question is asking to choose among the following choices that states the equation of the line that passes through (4,2) and is parallel to 3x-2y=-6, base on my calculation and further analysis, I would say that the answer would be y=-3/2x+8. I hope you are satisfied with my answer and feel free to ask for more