What is the equation of the line that passes through (4, 2) and is parallel to 3x - 2y = -6?
A.
3
y=--x+8
2
B.
3
y = -x-4
2
C.
y = -X
2
D.
2
y = -x-4
3

Unfortunately I can't read your answer options properly. The copied text is just too messed up. But hopefully the step-by-step calculation will help you.

Lemme know if it worked for you and if you have further questions.

Step-by-step explanation:

3x - 2y = -6

can be rewritten as

2y = 3x + 6

or simpler

y = 1.5x + 3

we know that it's parallel to this line, but we don't know how much lower or higher the new line will be, so let's set "+3" as an unknown variable.

y = 1.5x + b

(the letter b is now what we try to solve for)

now let's plug in the x-/y-Informations of the given point

2 = 1.5 * 4 + b

2 = 6 + b

-4 = b

so the new line is

y = 1.5x -4

(the given point lies on that line and it's parallel to the other line)

let's multiply everything by two to get closer to the original format

2y = 3x -8

it could also be expressed as

2y = -(-3x+8)

(in hope that this may help for choosing an answer option)

please clean up the text of questions before posting next time

(would really appreciate the brainliest)

bru

step-by-step explanation: