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

a y= 2x+6

b y= -2/3x +5/3

c y= 2x+3

d y= 2/3x+5/3

Verified Answer :

Here, Equation: 2x + 3y = 6
3y = -2x + 6

Divide both sides by 3, 
y = -2/3x + 2

Here, Slope = -2/3 and it would be same for that line which is parallel to it.
So, y - 3 = -2/3 (x + 2)
y - 3 = -2x/3 - 4/3
y = -2x/3 + 5/3

In short, Your Answer would be Option B

Hope this helps!

The equation of the line that passes through (–2, 3) and is parallel to 2x + 3y = 6 would be y = -2x/3 + 5/3.

How are parallel straight lines related?

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.

Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

We have been given an equation

Equation: 2x + 3y = 6

3y = -2x + 6

Divide both sides by 3,

y = -2/3x + 2

Here, The Slope = -2/3

The slope would be the same for that line that is parallel to it.

So, y - 3 = -2/3 (x + 2)

y - 3 = -2x/3 - 4/3

y = -2x/3 + 5/3

Hence, The Answer would be Option B.

Learn more about parallel lines here:

https://brainly.com/question/13857011

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